MTZ² v1.0 Lite: Scientific Reference Manual and Experimental Protocols in 2D/3D/4D Bioimaging

Where to Find Everything on Screen

Orientation before methodology. Analysis wizards are selected from the Surpass Tree (🌳 Surpass Tree tab) and open in the adjacent ⚙️ Wizards tab: clicking an item in the tree automatically switches to that tab.

User Account & Privacy

MTZ² authenticates via Google Account at intelligentia.dev/mtz+mgd/: click Sign in with Google. New accounts are provisioned instantly without passwords to manage. Your raw microscopic datasets are never uploaded to external servers: data is opened and rendered strictly client-side within your browser sandbox.

• Avatar Pill (top-right corner): My Account and Sign Out. On mobile devices, located in the ⋯ More action sheet.
• My Account: Displays all stored profile parameters (name, email, access timestamps), exports session data to JSON, and provides one-click account deletion.
• Support & Inquiries: Help › Contact & Support, or direct inquiry via imagine@intelligentia.dev.

Complete Examples, Step by Step

Routine workflows from start to finish. Each recipe can be followed independently without having read the rest of the manual.

R.1 Counting Nuclei and Measuring Area

R.2 Curating Results Manually

R.3 Comparing Two Markers

R.4 Preparing a Publication Figure

R.5 Exporting 3D Meshes for 3D Printing (STL) and CAD / Blender (OBJ)

R.6 Loading Native Zeiss (.CZI) and Leica (.LIF) Formats Without Conversion

R.7 Axial Penetration and Aberration Diagnosis in Maximized View (Canonical Views)

R.8 Ergonomic Multi-Monitor Workspace Setup (PanelManager)

R.9 FAIR Traceability and Multi-Slice Series Verification in Header (SAMPLE:)

What's New in this Version (Builds 018893 to 018900)

Summary of enhancements in this release, including the underlying scientific justification and relevant manual sections. All enhancements were verified with objective quantitative benchmarks prior to deployment; cited metrics reflect observed empirical validation data.

AI Assistant: Biomedical Expert and Autonomous Agent in the Suite

The assistant serves two simultaneous roles. As a consultant, it provides scientific rationale with the domain expertise of a doctoral researcher in optical microscopy, anatomical pathology, microbiology, quantitative cell biology, genetics, and biostatistics. As an operator, it autonomously executes analysis pipelines within the suite: loading data, segmenting, counting, measuring, cross-correlating channels, tracking 4D trajectories, generating publication figures, and drafting methodology sections, evaluating step results before executing subsequent actions.

Setup and Connection

1. Open via the AI tab in the right panel, the 🤖 AI Assistant button in the header, or Ctrl/⌘ + K. In voice mode, audio queries route directly to the agent.
2. Click ⚙ to open the AI Hub, choose your provider, enter your API key and model identifier, then click Test and Save. The green indicator in the panel header confirms readiness.
3. Type or dictate your prompt. Enter sends; Shift + Enter adds a new line; Stop (or Esc inside the prompt box) halts the agent immediately.

Capabilities & Supported Tools

Actions that destroy or overwrite user data — closing images, overriding results, clicking deletion triggers — require explicit user confirmation via an on-screen dialog card. If the user clicks «No», the assistant immediately aborts that action.

Autonomous Execution Loop

Requests are resolved iteratively: the model determines required tool invocations, the suite executes them in the browser engine and returns quantitative results, and the model determines subsequent steps until the objective is fulfilled (up to 16 iterations per prompt). Each intermediate step renders in chat with its output. Wizard input fields update live in the UI, allowing researchers to inspect and manually adjust parameters.

• Zero numerical hallucination: Metrics are exclusively reported from tool execution outputs. Unmeasured values are explicitly flagged as such.
• Measurements vs Geometric Models: Surface areas and volumes are extracted from voxel isosurfaces; equivalent diameters assume spherical/circular geometry.
• Calibration Auditing: Flags when physical metric units depend on unverified default voxel calibrations.
• Biophysical Limitations: Highlights border-truncated objects, intensity saturation, small sample sizes (n), axial elongation, and pseudoreplication.
• Literature Grounding: Formally cross-references theory and methods with sections in this Manual.

Domain-Specific Query Examples

Troubleshooting

Automatic Segmentation on Load: Methodology, Validation & Boundary Limits

Upon loading an image, MTZ² autonomously segments objects within the nuclear/primary signal channel and reports quantitative measurements without requiring manual threshold adjustments. Parameters are not fixed defaults: they are measured dynamically from each individual image, as pixel nuclear footprint, background noise, and illumination gradients vary across objectives, detectors, staining protocols, and tissue architectures. With static parameters, reference pipelines fail to isolate intact cellular morphology (F1 = 0.005).

Execution Sequence on Load

1. Target Channel Selection: Matches metadata labeled DAPI, Hoechst, DRAQ5, or Nucleus; lacking labels, selects emission < 500 nm or blue pseudocolor; otherwise resolves to the channel with the highest integral signal. Derived mathematical channels and blank background channels are strictly excluded.
2. Dynamic Parameter Auto-Tuning: Runs in an isolated Web Worker thread (zero main-thread UI freezing): extracts characteristic object diameter, optimal Gaussian smoothing σ, local threshold partition, and seed persistence.
3. Segmentation & Morphometry: Measures each segmented object: surface area (2D) or volume (3D), equivalent spherical/circular diameter, mean and peak intensity, and centroid spatial coordinates.
4. Interactive Visual Representation: In 2D, renders crisp yellow vector contours tracing pixel boundaries without masking fluorescence intensity; in 3D, constructs Marching Cubes isosurfaces. The Surfaces Wizard reports empirical parameters with the badge «Parameters measured from this image».

Mathematical Methodology

1. Representative Working Plane: For 3D stacks, targets the optical plane with maximal integrated intensity. If plane dimensions exceed 1024 px, downsamples via area-averaging blocks (never nearest-neighbor decimation) solely to calibrate parameter metrics.
2. Empty Field Rejection: Global Otsu thresholding identifies two populations separated by contrast $\Delta$. Uncorrelated photonic noise is estimated via robust median absolute difference between adjacent pixels: $$\hat\sigma = \frac{1.4826\,\operatorname{median}\lvert I_{x+1}-I_x\rvert}{\sqrt{2}}$$ If $\Delta < 4\hat\sigma$, the FOV is flagged as an empty field: «no objects emerge from background noise floor». Prevents false-positive artifact hallucination in empty culture wells.
3. Gaussian Smoothing Sweep: Evaluates filter kernels $\sigma \in \{0, 1, 1.5, 2, 3, 4, 6, 8, 12\}$ pixels (terminating when $\sigma > d/5$). For each kernel, thresholds and computes region isoperimetric compactness, $C = 4\pi A / P^2$ (area-weighted median). Selects the minimal $\sigma$ achieving 95% peak compactness: eliminates high-frequency sensor grain without merging adjacent nuclei.
4. Characteristic Equivalent Diameter: $d = 2\times$ area-weighted median of maximum Euclidean distance transform depths across regions.
5. Adaptive Local Thresholding: Evaluates local Otsu partitions within sliding tiles of side $3d$, compensating for uneven field illumination. If candidate objects exceed 1/6 total FOV (whole organism autofluorescence or thick tissue halo), tiles reduce to 1/8 FOV.
6. Persistence-Based Watershed Separation: Watershed seeds originate from Euclidean distance transform peaks whose topological persistence exceeds $h = 0.2\,r$ (h-maxima transform); flooding runs over the gradient mask. Separates abutting nuclei along physical concavities rather than artificial straight lines, preserving seeds for small intact nuclei.
7. Biological Size Gating: Enforces area boundaries from 5% to 400% of nominal area $\pi (d/2)^2$ in 2D, and 5% to 600% nominal volume in 3D. For a 10 µm nucleus: bounds span 3.9 µm² to 314 µm².

Empirical Benchmark Validation

Validated against expert ground-truth manual segmentations from standardized public bioimage repositories across withheld test splits. Detections count as true positives when intersection-over-union (IoU) with ground truth exceeds 0.5: $$\text{IoU} = \frac{|A\cap B|}{|A\cup B|},\qquad P = \frac{TP}{TP+FP},\quad R = \frac{TP}{TP+FN},\quad F_1 = \frac{2PR}{P+R}$$

Evaluated across 29,438 expert-annotated nuclei. Persistence-based topological separation outperformed static distance-peak spacing in 297 of 374 benchmark images, and non-cellular negative controls correctly flagged zero objects.

Manual Intervention Criteria

• Adjusting any slider (steps 2–5 in wizard) switches to explicit manual override and dismisses the auto-tune badge. Click «✨ Auto-adjust to this image» to recalculate.
• Manually moving the threshold slider converts algorithm to fixed intensity isosurface mode.
• Faint nuclei in dense tissue: local Otsu may underestimate edges; lower threshold slider or decrease tile dimensions.
• Cytoplasmic or membranous markers: algorithm targets compact convex morphology; utilize Random Forest Classifier or manual 2D vector contours.
• Diffraction-limited sub-resolution foci (endosomes, FISH signals): use Spots Wizard rather than Surfaces.

The preceding benchmark applies to 2D fields. In 3D volumes, Gaussian smoothing enforces identical physical σ in micrometers across all three axes, adjusting voxel kernel radius along Z when axial step size exceeds lateral pixel dimensions. Prior to Build 018900, axial smoothing used identical pixel kernel sizes: with $dx = 0.2\,\mu\text{m}$ and $\Delta z = 1.0\,\mu\text{m}$, axial filtering was 5× stronger than intended, artificially merging adjacent nuclei along the optical axis. In a synthetic 3D ground-truth phantom (42 nuclei/scene, chromatin texture, confocal PSF, Poisson noise; $\Delta z \in \{0.3, 0.6, 1.0\}\,\mu\text{m}$), anisotropic correction improved F1 from 0.738 to 0.982 for separated nuclei and from 0.668 to 0.937 for axially stacked nuclei, increasing mean IoU from 0.71 to 0.84 and dropping axial merge errors from 4.2 to 0.5 per stack. 2D calculations are unaffected.

Faithful Visualisation: Raw Acquisition Fidelity (2D, 3D & 4D)

Quantitative bioimaging is interpretable only if on-screen visual representations correspond strictly to photon fluxes registered by the detector. MTZ² renders images free from undeclared non-linear transformations and verifies pipeline integrity through objective bit-level tests against raw files.

2D Planar Imaging

• Linear Dynamic Range: Bypasses sRGB gamma distortions and covert contrast stretching. Files initialize adopting display windows stored in metadata — in Zeiss CZI, adopts native Zen channel LUTs, min–max black/white points, and gamma; in RGB, spans full dynamic range — falling back to robust automatic percentiles (0.1% low / 99.9% high saturation clip), mirroring standard desktop scientific imaging suites. Min–max defaults in 12–16 bit microscopy render near black due to sparse cosmic ray outliers; Auto and Full toggles adjust visual stretch without altering underlying raw voxel values.
• Per-Channel LUTs & False Color Palettes: Standard monochrome or scientific colormaps (Grayscale, Fire, Viridis, Magma, Inferno, Turbo) combined via additive physical blending. Single-channel colormaps reveal subtle intensity gradients lost in monochrome displays; embedded Leica and Zeiss palette tables apply automatically.
• Native Resolution & Interpolation: Preserves full pixel resolution up to GPU hardware limits. Zooming out uses trilinear mipmapping to prevent moiré aliasing; zooming in renders nearest-neighbor texels, avoiding interpolation of synthetic intensities.
• File Coordinate Orientation: Matrix row 0 maps to viewport top in 2D, maintaining strict parity with 3D orientation.

3D Volume Rendering Engine

1. Native Volumetric Resolution: Renders up to GPU hardware limits (standard 3D texture dimensions: 2048³ voxels) within a dedicated VRAM budget (512 MB desktop; 128 MB mobile/integrated). When downsampling is required, decimation targets the finest spatial axis first: in XY, scales by the exact fractional factor to meet bounds (a 4969 × 6254 px mosaic downsamples to 1628 × 2048 with factor 3.05, whereas integer factor 4 would over-decimate to 1243 × 1564); in Z, preserves integer optical planes. In Blend mode, downsampled voxels compute local averages; in MIP mode, voxels preserve local maxima, ensuring sub-resolution single-voxel point emitters are never lost. Large volumes exceeding 2048 px render downsampled in 3D (quantitative analysis runs at 100% native resolution); inspect critical features in 2D or Orthogonal Slicers at full native resolution.
2. Bit-Depth Preservation: High-bit acquisition data (12, 14, 16 bits) are stored in 16-bit half-precision floating-point textures (quantisation error < 1 count in 12-bit data; standard 8-bit textures produce 8-count banding under narrow display windows). 8-bit acquisitions load losslessly.
3. Premultiplied Optical Color: In MIP mode, rendered on-screen intensity tracks data linearly (low intensities: 24.5 → 25.0; midtones: 96.1 → 95.4 levels without artificial stretching). Eliminates midtone dimming artifacts common in legacy WebGL ray-marchers.
4. Physical Ray-Marching Opacity: In Blend mode, computes attenuation along physical optical path lengths (accounting for ray direction in anisotropic voxels), applying a quadratic ramp to prevent background autofluorescence from obscuring deep internal structures.
5. Jittered Ray Sampling (Elimination of Woodgrain Rings): Ray sampling starts with per-pixel stochastic dithering, accompanied by adaptive refinement (up to 8 samples) at volume boundary entry points. During interactive camera rotation, ray-step intervals adapt to maintain high framerates; on release and during figure export, high-sample supersampling renders a converged frame. Eliminates concentric dark/light sampling rings («woodgrain artifacts») absent in raw data. In test phantoms with coarse 10-voxel step sizes, image PSNR improved from 28 to 46 dB relative to a 1000-step ground-truth render.
6. High Axial Anisotropy (Coarse Z-Sampling): When axial spacing greatly exceeds lateral pixel size (e.g., whole-organ light-sheet with 100 µm slice intervals and 1.9 µm pixels), slices represent thick optical slabs and curved organ surfaces present stepped contours resembling topographic contour maps. This reflects physical sampling limits, not rendering defects. Standard linear interpolation produces harsh banding edges; in Blend mode, when Z-step exceeds 4× in-plane pixel size, MTZ² applies a cubic B-spline along Z, smoothing slab edges without synthesizing artificial structures (attenuating isolated single-slice signals to 2/3 peak). MIP mode strictly maintains linear interpolation to preserve photometric peak intensities. Configure via Properties › Inter-slice (Blend): Auto or Linear. Where surfaces run parallel to the optical axis, step profiles remain visible; inspect fine cellular architecture in native 2D slices.
7. Interactive Fluidity: If full-resolution ray-marching exceeds ~33 ms/frame, interactive rotation drops to half-resolution (1/4 ray count), immediately executing a high-precision converged pass on mouse release. Subsequent rotations on that volume initialize in fast mode. On an Apple M4 with Retina display and a 1628 × 2048 × 56 light-sheet stack: interactive framerates rose from 12 to 43 fps during rotation, with a 360-step converged final pass rendering in 0.3 s on release.

Choosing Between Blend and MIP

• MIP (Maximum Intensity Projection): Ideal for sparse, bright fluorescent structures — puncta, vesicular trafficking, dendritic spines, microvasculature. Displays peak intensity along the line of sight without obscuring internal nodes, but sacrifices depth occlusion cues.
• Blend (Alpha Compositing): Essential for evaluating 3D spatial organization, tissue boundaries, and anatomical occlusion. Raise the display window black level above the specimen background noise floor to prevent hazy volumetric occlusion.

4D Dynamic Time-Lapse Series

During 4D playback, each timepoint loads its dedicated 3D volumetric frame, dynamically updating isosurfaces if channel parameters vary. Elapsed display time calculates as timepoint index × interval, adopting the acquisition delta declared in the Tracking Wizard (matching kinematics calculations).

Biomedical Applications: Solved Case Studies by Discipline

Standard biomedical research workflows solved from hypothesis to publication: acquisition guidelines, MTZ² execution steps, AI Assistant prompt equivalents, reporting standards, and mandatory negative/positive controls. Numerical values in examples are illustrative; clinical staging criteria must be cross-referenced against current authorized clinical guidelines.

Nyquist Sampling Criteria by Specimen Type

Theoretical confocal resolution (1.0 Airy pinhole): lateral $d_{xy} \approx 0.51\,\lambda/\mathrm{NA}$; axial $d_z \approx 0.88\,\lambda / \left(n - \sqrt{n^2-\mathrm{NA}^2}\right)$. Nyquist criterion dictates voxel dimension $\le d / 2.3$. For a 63×/1.40 oil immersion objective ($n = 1.518$) at 520 nm emission: $d_{xy} = 189$ nm and $d_z = 491$ nm, requiring pixel pitch $\le 82$ nm and axial step $\Delta z \le 214$ nm.

Histopathology: Ki-67 Proliferation Index via Immunofluorescence

Microbiology: Bacterial Viability & Biofilm Architecture

Genetics & Cytogenetics: Interphase FISH Analysis

Cell Biology: Mitotic Index & Chromatin Condensation

• Segment nuclear volumes and sort the objects catalog by surface area and mean fluorescence intensity, or inspect feature distributions in Vantage 1D: condensed mitotic chromatin (prophase through anaphase) and apoptotic bodies present as hyper-dense, high-intensity punctate volumes.
• Train the Random Forest Classifier on annotated phenotypic exemplars and cross-validate against specific biomarkers (phospho-histone H3 for mitosis; cleaved caspase-3 or TUNEL for apoptosis).
• Report indices as proportions with 95% confidence intervals and clearly state the biological replicate sample size ($N$).

Neuroscience: Dendritic Arborisation & Spine Morphometry

• Filaments Wizard reconstructs neural arbors from soma centroids: quantifies total dendritic length, branch orders, bifurcation nodes, and concentric Sholl analysis profiles (intersections vs radial distance from soma); critical radius identifies peak arbor complexity.
• Dendritic Spine Classification: head volume, neck length, and morphological taxonomy (mushroom, thin, stubby, filopodia); diameter determined via transversal FWHM and inscribed maximal spheres.
• Enforce strict Nyquist axial sampling: optical stacks acquired with $\Delta z \ge 1\,\mu\text{m}$ introduce severe axial distortion in spine necks.

Microcirculation & Cell Motility Dynamics

• Microvascular Networks: trace endothelial markers (e.g., CD31, lectin) in Filaments Wizard → total length, branch density, and vessel caliber.
• Leukocyte/Erythrocyte Motility in 4D: Tracking Wizard using true physical inter-frame Δt → instantaneous velocity, track displacement, and Mean Squared Displacement (MSD: linear indicates Brownian diffusion; upward curvature denotes directed active transport).
• Verify calibrated acquisition intervals: kinetic rates scale directly with Δt.

Colocalisation in Pathological Protein Aggregation

Architecture and Foundations of the Surpass 3D/4D Engine

The Surpass Space environment in MTZ² projects raw biological matrices into a calibrated 3D affine space in physical metric units (micrometers, $\mu\text{m}$). The WebGL graphics pipeline incorporates two primary volumetric projection paradigms:

• Blended Emission/Absorption Raycasting: Numerically integrates photometric intensities along each camera sightline, simulating physical optical attenuation across thick tissue slices and 3D organoid spheroids.
• Maximum Intensity Projection (MIP): Extracts the maximal scalar value along each viewing ray onto screen pixels according to:

MIP mode is ideal for resolving dendritic arbors, microvascular capillary networks, and cytoskeletal actin filaments exhibiting high contrast over dark background.

In biological fluorescence imaging, uninformative dark background routinely comprises 75% to 92% of total volume. The WebGL volume shader (gpuVolume.js) evaluates if $\max(\text{RGBA}) < 0.002$ and advances with double-step ray increments, skipping expensive trilinear texture lookups and gradient calculations. This accelerates interactive rendering by 3× to 5×, sustaining 60 FPS.

Files stream slice-by-slice without preloading raw gigabyte payloads into heap memory. Massive volumes segment and detect spots in overlapping spatial blocks with boundary margins, with background noise thresholds and characteristic scales computed over the global dataset: yielding bit-for-bit identical results to whole-volume processing. Marching Cubes meshes slice-by-slice (identical topology, vertex-by-vertex, with minimal RAM overhead), colocalisation omits 8-byte/voxel duplication, and cryptographic SHA-256 signatures calculate in chunks.

The WebGL 3D texture renders at native data resolution up to GPU texture limits (typically 2048³ voxels) within available VRAM — otherwise downsampling via box filtering (Blend) or local maxima (MIP), storing high-bit data in 16-bit float textures. Quantitative analysis operates strictly on raw unbinned native voxel arrays within allocated image memory (1.6 GB default, expandable to 8 GB on import); if data exceeds budget, XY downsampling triggers with explicit provenance declaration. Images exceeding 512 Mvoxels or 1 GB/channel skip automatic background segmentation on load (exceeding 128 Mvoxels disables live threshold re-run): segmentation triggers explicitly via Create Surfaces without locking the main browser thread.

Tens of thousands of detected subcellular vesicles and synaptic spots render through a single unified hardware buffer in a single GPU draw call (1 draw call), compressing CPU overhead from 45 ms to 0.3 ms per frame.

Data Loading, Import Protocol & Physical Calibration

This is the foundational chapter for publication fidelity. All quantitative metrics expressed in $\mu\text{m}$, $\mu\text{m}^2$, and $\mu\text{m}^3$ represent raw voxel counts multiplied by physical calibration factors. Uncalibrated errors manifest not as software crashes, but as misleadingly plausible numerical inaccuracies.

Validation: The TIFF reader matches tifffile bit-for-bit across 12 validation suites (compression codecs, predictors, BigTIFF 64-bit offsets, big-endian byte orders, planar RGB, tiled TIFFs, hyperstacks); CZI and LIF parsers match czifile and readlif across synthetic specification files and production acquisitions: 5 CZIs (3 Zeiss Lightsheet with multi-angle/dual illumination or tile mosaics; one 32-tile 4.5 GB mosaic; one 5-channel field) and 2 multi-series LIF projects (17 series). On first loading data from a new instrument, verify dimensions and calibration against vendor software.

• Zero File Size Cap: Streams slice-by-slice (bypassing legacy 2 GB browser limits).
• Image Memory Ceiling: Automatically defaults to 20% of browser heap allowance (typically 1.6 GB desktop; 0.5 GB mobile). In the import dialog, allocate 3–4 GB on 16 GB machines and 6–8 GB on 32 GB workstations. Datasets exceeding allocation downsample in XY with formal declaration.
• Analysis Overhead: Peak processing operations require approximately 2.4× base image memory. Absolute channel limit: 2³¹ − 1 voxels.
• Block Partitioning: Volumes exceeding 16 Mvoxels/channel segment and exceeding 32 Mvoxels detect spots in overlapping chunks, matching global results bit-for-bit. With multi-threading, chunks distribute across Web Workers. 630 MB volume: 1135 objects segmented in ~13 s from file selection, spots in ~14 s; 2.4 GB stack opens and processes in ~15 s.

All acquisition timepoints import seamlessly (OME-TIFF, TIFF hyperstack, LSM, CZI, LIF), and embedded frame delta (Δt) routes directly to playback controls and the 4D tracking engine, computing velocities and diffusion coefficients in physical µm/s without manual entry. Total image memory encompasses all timepoints.

Voxel dimensions cannot be recovered from raw PNGs. Extract values directly from microscope acquisition software:

• Leica LAS X: Acquisition → Format → Pixel size
• Zeiss ZEN: Info → Scaling (X/Y/Z)
• Nikon NIS-Elements: Calibration → Recalibrate
• Olympus cellSens: Image properties, Calibration property field

The application prompts for calibration before loading, displaying the resulting bounding grid, effective voxel dimensions, and physical FOV in real time. Default values are permanently flagged as assumed in provenance records and the Methods paragraph.

Color consumer photographs store RGB triplets interleaved within each pixel. Confocal stacks do not: each channel is stored as an independent greyscale page within the container, interleaved across optical Z-planes. A 5-channel stack across 20 focal planes comprises 100 distinct TIFF pages.

• With OME-XML: De-interleaves automatically according to SizeC, SizeZ, and DimensionOrder. Preserves native channel labels.
• Without OME-XML: Interleaving cannot be inferred from raw pixel bytes; the dialog prompts to declare channel count. Lacking input, pages default to single-channel Z-slices with explicit warnings.
• Planar RGB: Channels reside within pixel byte tuples.

Arbitrary multi-spectral acquisitions are supported without artificial channel count ceilings.

When downsampling a stack in XY, physical voxel dimensions scale by the identical inverse factor simultaneously:

A $2048 \times 1536$ px field at $0.104\ \mu\text{m}$/px preserves its exact $212.992 \times 159.744\ \mu\text{m}$ physical dimensions across any decimation factor. Aspect ratios are strictly invariant; rectangular fields are never distorted into squares.

Loading, Mapping & Analysis of Biological Sequences (FASTA / GenBank)

In correlative microscopy and quantitative fluorescence assays, fluorophores originate from recombinant genetic fusion constructs (e.g., EGFP-Actin, mCherry-Tubulin, Histone H2B) or hybridizing oligonucleotide probes (smFISH / MERFISH).

MTZ² integrates the SequenceLoader engine to parse sequence records in standard FASTA (.fasta, .fa, .fna, .faa) and raw text formats.

>EGFP_Human_Actin_Fusion_Construct [Homo sapiens / A. victoria] Ex:488nm Em:507nm
MVSKGEELFTGVVPILVELDGDVNGHKFSVSGEGEGDATYGKLTLKFICTTGKLPVPWPTLVTTLTYGVQ
CFSRYPDHMKQHDFFKSAMPEGYVQERTIFFKDDGNYKTRAEVKFEGDTLVNRIELKGIDFKEDGNILGH
KLEYNYNSHNVYIMADKQKNGIKVNFKIRHNIEDGSVQLADHYQQNTPIGDGPVLLPDNHYLSTQSALSK
DPNEKRDHMVLLEFVTAAGITLGMDELYKMDDDIAALVVDNGSGMCKAGFAGDDAPRAVFPSIVGRPRHQ

• Biopolymer Classification: Automated recognition of DNA, RNA, or Polypeptide (Protein).
• Estimated Molecular Mass ($M_w$): Calculated in kiloDaltons (kDa) based on empirical residue weights ($\sim 330\,\text{Da}$/nt for DNA, $\sim 110\,\text{Da}$/aa for proteins).
• GC Content (%): Evaluates thermodynamic duplex stability and nucleotide compositional bias in transgenic constructs.
• Chromophore Identification: Identifies conserved autocatalytic tripeptide fluorophore motifs (such as Thr65-Tyr66-Gly67 in EGFP and Met66-Tyr67-Gly68 in mCherry), mapping the sequence to its corresponding spectral detection channel.

Confocal Optics, Nyquist-Shannon Sampling & Axial Focal Shift Correction

Spatial resolution in fluorescence optical microscopy is governed by light diffraction and the 3D Point Spread Function (PSF):

To eliminate spatial aliasing artifacts, the physical voxel grid must satisfy the Nyquist-Shannon sampling theorem:

Multi-Channel Management & Spectral Display Adjustment

In the 🎨 Channels LUT tab, researchers configure photometric response transfer functions for each fluorophore:

• Initial Display Window: Adopts settings stored in file metadata (in Zeiss CZI, adopts native Zen LUTs, display bounds, and gamma; in RGB, spans full dynamic range) or defaults to automatic robust percentiles (0.1%–99.9%). Auto and Full buttons adjust windows on demand; in MIP mode, Auto calculates directly over the maximum intensity projection, preventing dense specimens from rendering over-saturated white.
• Color Tables & Palettes: Channel Color or scientific pseudocolor scales: Grayscale, Fire, Viridis, Magma, Inferno, or Turbo. For single-channel acquisitions, pseudocolor scales reveal subtle intensity gradients indiscernible in monochrome.
• Redundant LUT Resolution: If metadata assigns identical colors to distinct channels, the panel triggers an advisory and provides Distinct Colors to separate them (selecting maximally distant perceptual hues).
• Dynamic Range (Min/Max Clipping): Suppresses non-specific background autofluorescence (black point) while preserving contrast across bright fluorescent structures (white point).
• Gamma Transfer ($\gamma$): Non-linear photometric transformation $I_{\text{out}} = I_{\text{in}}^\gamma$. Values $\gamma < 1.0$ enhance faint dendritic arborisations without saturating cell somas.
• Real-Time Mini-Histograms: Instant visual verification of intensity distributions to detect detector clipping or photomultiplier tube saturation.

Surfaces: Extracting 3D Objects from Fluorescent Signals

Surfaces is the central volumetric morphometry module. It converts raw channel voxel intensities into quantified objects: enumerating elements, measuring physical metrics, and cataloging items for individual curation. This provides the primary pipeline when handling dozens, hundreds, or thousands of cells without manual tracing.

6.1 The Five Pipeline Steps

The wizard is located under Wizards › 🧊 Surfaces:

1. Source Channel: The fluorescent signal from which object boundaries emerge.
2. Gaussian Smoothing: Suppresses Poisson noise grain prior to isosurface extraction.
3. Intensity Threshold: Delineates authentic fluorescent signal from background noise floor.
4. Separation of Touching Objects: Watershed topological partitioning based on characteristic diameter.
5. Size Gating (Volume / Area Filter): Excludes sub-resolution debris and multi-cellular aggregates.

6.2 Protocol Example: Counting Nuclei

6.3 Measured Biophysical Values vs Geometric Models

Surface area and volume are direct physical measurements: computed from the raw count of segmented voxels multiplied by calibrated physical voxel dimensions, free from geometric shape assumptions. The same applies to mean, integrated, and peak intensities. The equivalent spherical diameter is a theoretical model — assuming ideal spherical or circular geometry — and is explicitly tagged as such; bounding spheres in the 3D viewport represent equivalent models, not true irregular biological boundaries.

If calibration is incorrect, numerical counts remain valid while absolute $\mu\text{m}^3$ volumes scale erroneously. Without physical calibration, work strictly in voxels.

6.4 Polygonal Mesh Construction

Topological isosurfaces are generated via Marching Cubes (Lorensen & Cline, 1987) applied directly to the segmented object binary mask rather than raw scalar intensities. This guarantees that visual meshes correspond strictly to segmented voxel boundaries. Meshes serve visual rendering; quantitative values derive from discrete voxel integration.

6.5 3D Mesh Export for 3D Printing (STL) and CAD / Blender (OBJ)

Generating surfaces activates two high-fidelity 3D mesh export options:

• Export STL (3D Printing): 32-bit Little-Endian binary STL with 80-byte header and facet normals. Guaranteed 100% watertight manifold topology ready for immediate slicing in PrusaSlicer, Bambu Studio, or Cura. Slicers interpret $1\,\mu\text{m} = 1\,\text{mm}$, generating a physical macroscopic model at 1,000:1 magnification for tactile teaching and bio-fabrication.
• Export OBJ (CAD / 3D Modeling): Standard Wavefront OBJ geometry with real-world metric coordinates ($\mu\text{m}$), smooth vertex normals for continuous shading, and clean triangular topology. Ready for Blender Cycles/Eevee photorealistic rendering, anatomical animations, and scientific figures.

6.6 Real-Time Coverage Slider ($O(1)$ via CDF)

Percentage thresholding operates via logarithmic binary search over a pre-computed 16-bit Cumulative Distribution Function (CDF). In just 16 operations ($< 0.02$ ms), the interface updates thresholds dynamically without re-scanning raw volume data or stalling GPU raycasting.

Sub-Voxel Spot and Vesicular Particle Detection

Quantifies diffraction-limited fluorescent puncta (synaptic vesicles, endosomes, virions, stress granules, single-molecule mRNA) via scale-space blob detection:

1. Band-Pass Spatial Filtering: Difference of Gaussians (DoG, $k = 1.6$), with filter scale matched to expected spot radius via $\sigma = r / \sqrt{3}$ independently per axis: lateral radius $r_{xy}$ and axial radius $r_z = \text{axial elongation} \times r_{xy}$ (default 2×; confocal PSFs are 2–3× longer axially). Implemented as separable 1D convolutions with $O(nk)$ complexity.
2. 3D Local Maxima: Evaluates 26-voxel volumetric neighborhoods with deterministic plateau tie-breaking.
3. Sub-Voxel Coordinate Localization: 3D parabolic interpolation over the DoG response (using 3-plane Gaussian interpolation along Z when axial sampling is coarse). Localization accuracy on synthetic phantoms: 0.002 $\mu\text{m}$ (≈ 1.3% of a voxel).
4. Local Background Subtraction: Computes the median of an ellipsoidal shell situated between 2 and 3 radii from the centroid (annulus in 2D), strictly avoiding the spot's own diffraction tail.

Per-Axis Model Validation: Across 12 ground-truth benchmark scenes (PSFs elongated 2–4× in Z, steps 0.1 to 1.0 µm), mean F1 improved from 0.978 to 0.991 (worst-case from 0.892 to 0.935), with background subtraction error dropping from 34 to 2.5 gray levels, invariant to fine axial steps.

Filament Tracing, Neurite Outgrowth & Sholl Morphometry

The Filaments module reconstructs tubular biological branching structures — dendritic arbors, axons, microvascular capillaries — directly from raw image voxel data via geodesic medial centerline tracing (APP/APP2 algorithmic family, Peng et al.).

1. Thresholding & Distance Transforms: Distance transforms incorporate physical anisotropic voxel weights, yielding local radii in $\mu\text{m}$ rather than voxel units.
2. Automated Soma Root Identification: Resolves the global maximum of the distance map — corresponding to the thickest morphological node (cell soma in neurons).
3. Centered Geodesic Shortest Paths: Propagates through the segmentation mask while penalizing deviation from the medial ridge. Without medial penalization, shortest paths take diagonal shortcuts cutting corners along inner lumen walls.
4. Iterative Furthest-Point Tracing: Traced paths claim a tubular volume of influence; subsequent branches initialize from the furthest unclaimed node.

Path length integrates physical metric Euclidean distances through voxels: mathematically exact by construction, including oblique diagonals.

• Total Traced Length ($\mu\text{m}$), branch segment count, and bifurcation nodes.
• Longest Continuous Path ($\mu\text{m}$): primary arborisation axis.
• Mean Caliber / Radius ($\mu\text{m}$), measured directly from the distance transform.
• Fraction of total segmented structure topologically connected to the root soma.

Quantifies branching complexity by counting discrete branch intersections across concentric spherical shells of expanding radii centered on the soma centroid. Intersections are evaluated directly on the thresholded binary mask rather than the skeletal graph, ensuring mathematical independence from skeletonization heuristics. Reports peak intersection count $N_{\max}$, critical radius $r_c$, and enclosing radius $r_e$, exporting the complete raw profile for publication figures in R or Python.

Quantitative Fluorescence Colocalisation (Coloc)

Colocalisation analysis faces rigorous scrutiny during scientific peer review. MTZ² computes the complete suite of established orthogonal coefficients required by international reporting standards.

Evaluated across the entire ROI without intensity threshold masking, adhering to the mathematical definition of the statistic. Masking policies are declared explicitly in export summaries and Methods text.

Fits an orthogonal regression line $B = aA + b$ — orthogonal rather than ordinary least squares because both optical channels contain detector noise — descending the threshold along the regression slope until the population beneath exhibits zero correlation ($r \le 0$). The residual population above threshold constitutes the true correlated signal by construction, eliminating subjective visual thresholding.

Independent of absolute fluorophore intensity ratios: ideal when labeling efficiencies or quantum yields differ significantly between probes.

• Li's Intensity Correlation Quotient (ICQ, 2004): Bounded in $[-0.5, +0.5]$; $+0.5$ denotes dependent synchronous staining, $0$ indicates random distribution, and negative values reflect mutual exclusion.
• Spearman's Rank Correlation ($\rho$): Non-parametric rank correlation resilient against non-linear detector response. In monotonic non-linear relations, $\rho = 1.000$ vs $r = 0.916$: reporting both differentiates true biological association from detector saturation curves.

Traditional rank calculation via $O(N \log N)$ sorting (quicksort) previously froze the browser for over 35 seconds on $10^7$ voxel confocal volumes. MTZ² implements an $O(N)$ counting sort and prefix-sum cumulative histogram over 16-bit dynamic ranges. Rank ties are resolved analytically, reducing execution time from 35,000 ms to under 20 ms (>1,700× speedup) with bit-exact metrological accuracy.

High correlation does not establish specific molecular association: two independent markers filling the same compartment correlate by spatial confinement. The Costes randomization test permutes channel $B$ in spatial blocks matching PSF dimensions — disrupting spatial alignment while preserving local texture — evaluating empirical $p$-values. The pseudo-random generator is seed-deterministic: identical inputs consistently produce identical $p$-values.

4D Dynamics, Particle Tracking & Quantitative Kinematics

A temporal image series represents an experiment examining biological motility. Merely playing back frames measures nothing: quantitative bioimaging requires linking each individual object with its corresponding self over time.

Navigation and Workflow

1. Load a time-series dataset featuring multiple timepoints: Mitosis, Microvascular Network, or Phagocytosis from the top sample dropdown.
2. Left panel → 🌳 Surpass Tree tab.
3. Click ◯ 4D Trajectories. The panel automatically transitions to the ⚙️ Wizards tab, displaying the 🕑 4D Particle Tracking wizard.
4. Select the source channel containing motile objects and declare the inter-frame time interval ($\Delta t$) in seconds: this parameter converts coordinate displacements into physical velocities.
5. Click 🕑 Track Objects Over Time.

Kinematic summaries render beneath the trigger: reconstructed trajectories, mean velocity, track straightness, apparent diffusion coefficients, and an interactive Mean Squared Displacement (MSD) curve. Trajectories render as 3D vector polylines in the viewport.

Inter-frame spatial linking is resolved through global combinatorial assignment (Hungarian algorithm) rather than greedy nearest-neighbor heuristics.

The cost matrix incorporates cost boundary augmentations (Jaqaman et al., 2008) so that non-linking competes as a valid finite-cost option: when forcing an improbable jump exceeds a realistic penalty, the algorithm registers a track termination or birth. The gap-closing tolerance parameter prevents transient fluorescence blinking from fragmenting a continuous trajectory into false truncated tracks. Linking evaluates against active track tails across preceding frames.

With a user-declared maximum biological velocity ($v_{\max}$), the gating search radius is $R_{\max} = v_{\max} \cdot \Delta t$. In automated mode, gating defaults to 3× the median nearest-neighbor distance — using the median rather than the mean to prevent sparse rapid outliers from expanding search gates globally.

• Instantaneous and track-averaged velocity ($\mu\text{m}/s$) with standard deviation.
• Total trajectory path length vs net Euclidean displacement.
• Directional Straightness $=$ net displacement / total path length, bounded in $(0, 1]$: values approaching 1 denote directed active transport; values near 0 reflect confined Brownian wandering.
• Mean Squared Displacement (MSD): Evaluated across temporal lags ($\tau$), deriving apparent diffusion coefficients ($D$) via $\langle r^2\rangle = 6D\tau$.

Each trajectory renders as a 3D polyline pseudocolored by mean track velocity across perceptually uniform colormaps (avoiding red-green palettes). CSV exports provide population summaries, single-track kinematic rows, raw MSD coordinates, and comprehensive spacetime coordinates ($x, y, z, t$).

• Population Summary: Displayed beneath the wizard button (mean ± SD, straightness, duration, diffusion coefficient, and search radius).
• Per-Track Table: Right panel → 📏 Measurements tab: sorted table reporting velocity, displacement, straightness, and duration per trajectory.

Rather than computing an unconstrained dense $O(N^3)$ global cost matrix (8,500 ms/frame on dense fields), the engine exploits physical velocity limits $v_{\max}$ to establish a bounded gating window $R_{\max} = v_{\max} \cdot \Delta t$. A sparse bipartite graph is constructed and partitioned into independent connected components. Each subcomponent of size $k \ll N$ is solved via Kuhn-Munkres independently, reducing compute time to 2 ms per frame pair (>4,000× acceleration).

During 3D persistence watershed operations, transient TypedArray memory allocations were eliminated by recycling pre-allocated static typed buffer pools, preventing JavaScript garbage collection latency spikes and cutting watershed processing time by 70%.

Orthogonal Slicers and 3D Euclidean Metrology

The Ortho Slicer mode provides simultaneous, synchronized navigation across the three canonical Cartesian planes (XY axial, XZ coronal, YZ sagittal) of the calibrated volume.

1. Activate the ruler via 📏 on the floating toolbar. The cursor transitions to a crosshair and camera rotation is temporarily locked, preventing accidental viewpoint tilting while picking measurement anchors.
2. Click point 1, click point 2. Cyan spherical markers anchor each endpoint, connected by a dashed 3D line.
3. Upon registering the second endpoint, the physical distance logs and the anchor counter resets: subsequent clicks immediately initiate a new measurement pair rather than extending an unclosed polyline.
4. Logs accumulate in the Measurements tab, recording 3D spatial coordinates ($x, y, z$) for both endpoints.
5. Clicking 📏 again toggles ruler mode off and removes on-screen viewport pins while retaining tabular records.

Ray-Picking Intersection Hierarchy

1. Solid Reconstructed Geometry First: Ray-casting intersects first against active isosurfaces, spot meshes, and traced filaments. Intersections are exact and invariant to display transfer functions.
2. Volumetric Ray-Marching Fallback: If no solid polygonal geometry is present, the ray marches through raw voxel data, halting at the first voxel whose scalar intensity surpasses the display threshold — snapping directly to the first visible biological boundary.
3. If no signal is intersected along the sightline, no anchor is placed, reporting an explicit diagnostic warning rather than hallucinating arbitrary coordinates.

• 3D Viewport: Physical micrometers per on-screen pixel vary dynamically with camera distance ($h = 2d\tan(\theta/2)$). Consequently, the 3D scale bar rescales in real time during zoom adjustments.
• Orthogonal Slices: Scale calculates from physical calibration metrics.

Scale bar lengths round to standard 1, 2, or 5 multiples of ten ($10^n$); nanometers below 1 µm, millimeters above 1000 µm.

Measurements export to CSV with 3D endpoint coordinates, surface target classifications, and ISO 8601 timestamps, preserved across sessions.

Free 3D rotation can obscure axial penetration gradients and symmetry. The maximized viewport provides one-click canonical orthographic alignment triggers:

• 🌐 Isometric 3D: Standard $45^\circ$ axonometric perspective, preserving spatial depth cues.
• ⬆️ Top View (XY): Orthographic axial projection perpendicular to the optical axis, matching conventional confocal planar views.
• ➡️ Frontal Plane (XZ): Coronal transversal cross-section. Facilitates direct visual inspection of axial photonic decay $I(z)$ and optical scattering.
• ↗️ Lateral Plane (YZ): Sagittal view. Indispensable for evaluating focal shift elongation artifacts caused by coverslip refractive index mismatch.

For multi-monitor workstations and ultra-wide displays, side panels and the 4D timeline detach into floating viewports:

• Undock (❐): Transforms panels into glassmorphic floating windows with drag handles (⋮⋮) and resize corner grips (⤡).
• Keyboard Shortcuts: Alt+1 (Left Panel), Alt+2 (Right Panel), Alt+3 (4D Timeline), Alt+4 (3D Tools), Alt+5 (Header Menus), Alt+0 (Reset All to Factory Defaults).
• Retractable Edge Tabs: Closing a floating window creates a retractable edge tab to restore it with a single click. Window configurations persist in localStorage.

The SAMPLE: header block displays verified active dataset provenance:

• Multi-Slice Z-Stacks: Parses series prefixes and displays 📁 cell01 (40 slices), preventing confusing single 2D slices with physical 3D volumes.
• 2D vs 3D Verification: Single 2D slices are tagged 📷 name (2D extruded), cautioning that axial depth is synthetic and not citeable for biological volume.
• Status LED & Tooltip: Emerald green indicator (● Green) confirms valid physical data, with tooltip detailing matrix dimensions, channels, and calibration origins.

Provenance, Auto-Generated Methods & FAIR Principles

Verifying Production Build Integrity

The top header displays the active build identifier, e.g., Build 018778, incremented with each deployment.

The foremost driver of irreproducibility in quantitative microscopy is not algorithmic bugs: it is that months post-acquisition, exact threshold parameters, calibration scales, and raw file versions are lost. The Reproducibility module records complete audit trails during live analysis.

• Dataset Identity: Pixel dimensions, bit-depth, and SHA-256 cryptographic hash of raw voxel arrays. Two analyses citing identical hashes executed on identical data bytes.
• Physical Calibration Origin: Explicitly tags whether voxel dimensions derive from OME metadata, manual entry, or assumed defaults, alongside downsampling decimation ratios.
• Algorithm Parameter Logs: Records all wizard parameters alongside ISO 8601 timestamps.

Generates rigorous publication-ready scientific text with formal literature citations derived from executed operations. Every numerical parameter in the text emerges directly from analysis logs; zero metrics are hardcoded templates. Integrates standard citations (Lorensen & Cline 1987; Marr & Hildreth 1980; Manders 1993; Costes 2004; Li 2004; Bolte & Cordelières 2006; Sholl 1953).

Saves thresholds, channels, false-color LUTs, segmented objects, measurements, and camera coordinates into a portable .mtz2.json file or URL fragment.

Applies identical segmentation parameters across cohorts of image files, outputting structured tabular summaries with common sample prefix grouping. Output CSVs embed configuration headers reporting exact parameters used.

Reports sample size ($n$), mean $\pm$ standard deviation, 95% confidence intervals, median, and dynamic range.

Pressing Ctrl+S triggers offscreen rendering at specified high-DPI resolutions (3840 px long edge), computing effective print DPI for standard 85 mm single-column figures.

Metrological Measurement Instrument Validation

Commercial microscopy software packages rarely declare intrinsic algorithmic measurement errors, leaving researchers uncertain whether reported volumes carry 1% or 50% systematic error. MTZ² provides real-time client-side verification directly in your browser session.

Reproducibility → Validate Instrument synthesizes mathematical geometric phantoms — perfect spheres, cubes, border-clipped objects, sub-diffraction Gaussian puncta — processing them through the identical measurement pipelines applied to experimental data. Observed deviation against analytical equations represents true algorithmic measurement error.

This validation suite executes automatically during continuous integration builds (6 test suites, 131 assertions), halting deployment if numerical tolerances diverge.

Educational Mode: Practical Exercises with Known Ground Truth

Zero-install web architecture enables simultaneous classroom deployment across hundreds of university students. Educational mode provides synthetic laboratory specimens featuring exact analytical ground truth, allowing automated quantitative assessment of student measurements.

Each exercise generates synthetic specimens dynamically from mathematical equations with exact voxel calibrations. Each student session generates using a unique pseudo-random seed: every student receives distinct numerical ground-truth values preventing answer sharing, while instructors can regenerate the identical seed for grading.

Interactive Pixel Classifier: Segmentation by Interactive Brush Training

Scalar intensity thresholding separates features only when intensity distributions diverge. When biological structures share identical gray levels with surrounding background and are distinguishable solely by texture, spatial scale, or local morphology, thresholding fails regardless of fine-tuning. The Interactive Classifier addresses this by training directly on user annotations.

Navigation and Workflow

1. Left panel → 🌳 Surpass Tree → ◉ Classifier.
2. Select the target channel to segment.
3. Check Enable Brush. The viewport switches to synchronized orthogonal slice planes where brush annotations are drawn.
4. Under class Object, paint over obvious cellular structure; under Background, paint over empty extracellular space. To resolve multi-class targets, add classes via + Class.
5. Click Train & Classify.
6. Inspect classification predictions and paint corrective strokes exclusively where errors occur. Retrain.

Multi-Class Color Segmentation

Workflows are not restricted to binary foreground/background: define up to 8 discrete classes with individual color tags (e.g., Background, Cytoplasm, Nucleus, Plasma Membrane). The Random Forest partitions all classes simultaneously.

• Add Class: Click + Class.
• Rename: Double-click class label.
• Change Color: Click color swatch.
• Delete: Click × on hover; brush strokes clear and indices renumber.
• Paint: Click class row to activate brush.

Class 0 is permanently reserved for Background: the classifier requires explicit negative training examples of non-signal regions.

The Class to Quantify selector specifies which classified class converts into an isosurface for morphometric measurement. Re-measuring classes does not require retraining. Across a 3-layer concentric phantom, class concordance was 1.00, 1.00, and 0.98.

Multiscale Feature Descriptor Vectors

Raw voxel intensity alone cannot resolve complex phenotypes. Each voxel is parameterized across 13 multiscale spatial descriptors evaluated at three filter scales ($\sigma \in \{1, 2, 4\}$ pixels in XY, mapped to physical micrometers along Z): raw intensity, Gaussian smoothing, gradient magnitude, Difference of Gaussians (DoG), and local texture variance. The model identifies which descriptor best discriminates target classes.

Interactive correction requires instantaneous retraining cycles. Random Forests (Breiman, 2001) train in milliseconds on modest sample sizes, require zero hyperparameter tuning, and yield calibrated posterior probabilities. Deep neural networks require minutes and GPU clusters: impractical for interactive browser-based sessions. Empirical benchmark: 12 ms training latency on 302 annotated voxels.

Random Forests initialize with fixed pseudo-random seeds: identical training strokes yield deterministic segmentations. Training strokes persist in session files, and Methods logs record class counts, descriptors, sample sizes, and OOB scores.

Native Vendor Formats (Zeiss CZI & Leica LIF), 3D Mesh Export (STL / OBJ) & Acceleration Matrix

Direct binary streaming of Zeiss and Leica containers without prior file conversion, physical 3D mesh export for additive manufacturing, and high-performance algorithmic acceleration architecture.

Exporting to multi-file TIFFs from vendor workstations consumes disk storage and risks losing physical metadata ($dx, dy, dz$). MTZ² parses both proprietary binary container architectures directly slice-by-slice.

Reconstructed Marching Cubes isosurfaces export with metric precision:

Reproducible Workflow Recipes (.mtzwf), Batch Processing & Methods Reporting

Every executed analytical module appends a validated step to the active recipe (🔬 Reproducibility › 🔄 Workflows) with parameters, execution timestamps, and quantitative summary metrics. Recipes export in open .mtzwf JSON formats sealed by cryptographic signatures: $H = \text{SHA-256}(\text{JSON}(\text{steps}))$. Signatures verify on import; modified files are rejected.

In 📦 Batch, clicking 📂 Choose Files… executes active pipeline parameters across entire folder cohorts at native resolution (applying surfaces, spot detectors, colocalisation, and filament tracing). Results compile into a unified CSV with one row per specimen alongside data quality flags (border clipping, uncalibrated voxel assumptions, fragmented arborisation). Parameters are kept strictly identical across batch runs to preserve comparability across experimental cohorts.

3D Region of Interest (ROI) Bounded Detection

Restricts segmentation and detection of Spots, Filaments, or Secondary Cells strictly within the 3D volume enclosed by previously reconstructed biological isosurfaces, filtering out extracellular debris, non-specific background, and stromal artifacts.

Combines immediate $O(1)$ spatial bounding box rejection ($\text{AABB}(S)$) with discrete voxel inside-outside evaluations on the discretized volumetric mask $\mathcal{M}_S(x,y,z)$. In addition, computes exact orthogonal Euclidean distance to the bounding membrane: $d_{\perp}(\mathbf{p}, \partial S) = \min_{\mathbf{q} \in \partial S} \|\mathbf{p} - \mathbf{q}\|_2$.

Machine Learning: Exemplar-Trained Random Forest Classifiers

Under optical photobleaching, depth-dependent scattering, or autofluorescent pigments (lipofuscin, elastin), single global thresholds fail to resolve signal from noise. MTZ² integrates two Random Forest classifiers (Breiman, 2001) that train dynamically in the browser from user-annotated exemplars, reporting objective Out-of-Bag (OOB) error estimates.

Decision tree splits evaluate $m = \mathrm{round}(\sqrt{p})$ randomly sampled features per node, minimizing Gini impurity; class posterior probabilities correspond to tree vote fractions. OOB metrics evaluate training samples exclusively across trees where that sample was withheld. Under randomized labels, OOB accuracy collapses to 51.5% (random chance validation).

3D Channel Masking in Batch (Batch Channel Masking)

Generates a new optical channel isolating voxel intensities from another channel strictly inside (or outside) segmented biological objects, preserving identical data types and radiometric units; raw acquisition channels are preserved untouched. Upon generation, the panel reports fractional voxel volume and the fraction of total radiant intensity sequestered inside or outside target compartments (without background subtraction).

Vantage: Bio-Statistics & In Silico Image Cytometry

Vantage visualizes and statistically compares quantitative measurements extracted from the active image: segmented surfaces, spots, traced filaments, manual regions, dendritic spines, and 4D trajectories. If no objects have been segmented yet, it provides instructional guidance on running upstream wizards. Open via 📊 Vantage in the top header and close with ✕ Close Vantage or Esc.

The left hierarchy enumerates active object classes (e.g., dendritic spines: Mushroom, Thin, Stubby, Filopodia; classifier-filtered spots; complete vs truncated tracks). Unchecking an item excludes those entities from plots and hypothesis tests. Group By determines comparative cohorts: Type, Class, Provenance (derived, manual, or edited), or Population (gated cohorts). Modeled metrics (e.g., spot equivalent spherical volume) are marked with ⚠ beneath plots and with an asterisk (*) in tables.

For every segmented biological object, Vantage computes mean fluorescence intensity across all available channels over its discrete voxel mask (for spots, within its fitted radius). In multi-channel datasets, the 2D view opens with Channel 1 vs Channel 2 bivariate plots. Cytometric Gates are drawn directly onto the plot: Quadrants (single click places intersection crosshair, calculating four percentage quadrants), Rectangle (drag-to-draw), or Polygon (click vertices; double-click or click initial vertex to close; Esc cancels). Clicking 💾 Save Population registers the gate as a named population cohort; gated populations can be isolated in the 3D viewport, cross-compared in 1D views, and exported.

Validation: On a synthetic 3-channel phantom containing 220 cells across four known fluorophore proportions, auto-segmentation isolated all 220 cells and GFP/RFP cytometric quadrant gates reconstructed single-cell ground-truth proportions exactly (33 / 48 / 84 / 55).

Advanced Morphometry & Dual-Diameter Dendritic Spine Analysis

Overcoming the optical diffraction limit in sub-micrometric dendritic spine necks ($50 - 200\,\text{nm}$) through the decoupled synthesis of 3D Euclidean distance transforms (inscribed spheres) and orthogonal transversal Gaussian fitting (FWHM).

Training Hub, Arena Mode & Seven Specialized Workspaces

In silico simulation environment featuring analytical ground-truth phantoms, multi-volume comparative screening via Arena Mode, and 7 contextual workspaces tailored to distinct experimental paradigms.

Advanced Modules: AI Assistant, FAIR Evidence, Optical Restoration, AlphaFold, Voice, Audit, OME-Zarr & Live Sync

These advanced modules extend conventional bioimage visualization and morphometry. All features are fully functional in production: executing mathematical computations directly on your active datasets within declared operational parameters. Zero numerical values represent static placeholders.

Replaces legacy keyword matching with an autonomous agentic execution loop that directly triggers application tools, awaits quantitative outputs, and synthesizes empirical results (see AI Assistant chapter).

A single offline .html file: dataset identity (raw voxel SHA-256 hash), optical calibration, 1600 px figure render with physical scale bar, Materials & Methods text with LaTeX equations, comprehensive measurement CSV with provenance tags, Wavefront OBJ surface mesh (< 25 MB), and vector SVG Vantage charts. Unmeasured parameters display as «—». Omits raw gigabyte voxel payloads. Hashes evaluate over decoded voxel arrays: verify integrity by opening the same file in MTZ² and matching against the Reproducibility panel.

Observed image $O$ represents true specimen $x$ convolved with PSF $H$, plus background $b$ and Poisson noise. Richardson-Lucy deconvolution (Richardson, 1972; Lucy, 1974) computes the maximum-likelihood estimate via multiplicative iteration:

Enforces non-negativity while strictly conserving total radiant flux. Synthesizes a theoretical 3D Gaussian PSF (Zhang, Zerubia, & Olivo-Marin, 2007): $\sigma_{xy} = 0.21\,\lambda/\text{NA}$ and $\sigma_z = 0.66\,\lambda n/\text{NA}^2$ for widefield, each divided by $\sqrt{2}$ for confocal optics. Output compiles into a dedicated new channel («channel · RL n it.», 16-bit float); raw data is preserved. Evaluates each timepoint in 4D series. Summary panels report peak/background ratios, total flux ratios, iteration delta, and compute latency.

Validation: On a synthetic phantom (40 point emitters blurred by confocal PSF, Poisson noise), 20 iterations increased correlation with ground truth from 0.21 to 0.74 while strictly conserving total radiant energy (× 1.02).

Retrieves predicted protein coordinates from AlphaFold DB (EMBL-EBI) via UniProt accession IDs (transmitting solely the identifier code), computes residue-by-residue pLDDT confidence (>90 very high, 70–90 high, 50–70 low, <50 intrinsically disordered), and renders Cα backbone ribbons colored by pLDDT at segmented spot centroids. Proteins measure single-digit nanometers — far below optical resolution limits: structures render magnified with on-screen scale multipliers. The overlay is exploratory and illustrative.

In Local Voice Mode, direct speech commands control viewport orientation («frontal plane», «isometric»), channels («only green channel», «blue channel 60 percent»), rendering modes («MIP mode»), snapshot capture, and 4D playback. In AI Voice Mode, spoken queries stream directly to the autonomous assistant. Audio Privacy: Speech recognition executes client-side via the browser Web Speech API. No image pixels are ever transmitted.

Advisories diagnostic causes, provide corrective actions, and highlight relevant UI controls in the active panel. The auditor never modifies parameters autonomously. Identical advisories debounce for 60 seconds.

• Dynamic Range Saturation: Triggers warning if >5% of voxels in any channel reach maximum saturation (255 in 8-bit; max present in 12/16-bit), where intensity ceases to scale linearly with fluorophore concentration. Flags empty channels.
• Assumed Voxel Calibration: Alerts upon image load if voxel dimensions rely on unverified defaults.
• Sub-Noise Manual Thresholds: Warns when manual isosurface thresholds fall below channel background noise ($\mu + 1.2\sigma$) or approach peak saturation.
• Colocalisation Rigor: Recommends Costes statistical thresholding when manual thresholds are selected.
• Deconvolution Integrity: Rejects unphysical optics ($\text{NA} \ge n$), warns if iterations exceed 30, and verifies Nyquist compliance.
• Cross-Module Integrity: Prohibits correlating a channel against itself or derived channels; tracks size-excluded objects.

OME-Zarr (OME-NGFF 0.4 on Zarr v2 and 0.5 on Zarr v3) stores multi-dimensional pyramidal datasets chunked into compressed blocks. MTZ² parses directory schemas ($t/c/z/y/x$ axes, physical coordinate scales, channel names, OME-XML LUTs in omero) and reads chunk codecs: uncompressed, Blosc (BloscLZ, LZ4, Zlib, Zstd with byte/bit shuffling), Zstd, Gzip, and sharded v3 containers with crc32c integrity checks. Validated bit-for-bit across 25 official OME benchmark datasets.

Enables synchronized multi-user exploration of 3D biological specimens across workstations: one Host and up to 25 remote peers. All participants follow the presenter's camera viewpoint, channel toggles, LUT transfer functions, rendering modes, and 4D timepoints, with real-time 3D laser pointers, spatial markers, and collaborative notes. Peers do not require local image files: the host browser streams raw image payloads securely over encrypted connections, verified via SHA-256 voxel hashes.

Peer Data Streaming Architecture

• Peer-to-Peer WebRTC (DTLS Encryption): Standard transmission pathway. Image data routes directly between client browsers without passing through MTZ² servers; STUN servers (Cloudflare / Google) establish NAT traversal without inspecting data packets.
• HTTPS Turn Relay Fallback: Employed when corporate or hospital firewalls block P2P WebRTC traffic, or when serving more than 3 simultaneous peer streams. The host uploads a single encrypted copy, which peers download asynchronously. Relayed copies purge immediately on session closure or after 12 h idle.
• Full vs Adaptive Review Downsampling: Datasets up to 1 GB stream at 100% full bit-exact resolution (confirmed by matching SHA-256 signatures). Massive datasets exceeding 1 GB or streaming to mobile clients stream as an adaptive review copy (2× downsampled in XY; voxel metrics rescale so physical distances remain in $\mu\text{m}$). Review copies serve visual consultation; final measurements must execute on the native original.
• Transfer Speeds: Data streams compressed (reducing 16-bit payloads by 50–70%). Over standard 20 Mbit/s connections, 250 MB stacks transfer in <60 s; local gigabit LAN transfers complete in seconds.
• Session Lifecycle: Peer copies remain active in memory during the session. Clicking ⏹ Close for All immediately purges all received copies from remote client browsers.

• Anthropic Claude (claude-sonnet-5 default, claude-opus-5, claude-haiku-4-5): Recommended for complex multi-tool autonomous workflows and rigorous quantitative reporting.
• OpenAI (gpt-4o-mini, gpt-4o, o1): Broad general capability; compatible with institutional private API proxies.
• Google Gemini (gemini-2.5-flash-lite, gemini-2.5-flash, gemini-2.5-pro): High-speed interactive queries and generous rate allowances.
• Local Ollama Daemons (qwen2.5, llama3.1, mistral-nemo): Zero data egress; compliant with strict hospital and clinical patient data regulations.

Providers receive structured text metadata exclusively (conversational history, session dimensions, voxel calibration, quantitative measurements). Raw image pixels and 3D voxels are never transmitted. API keys persist solely in local client storage.

Quick Reference Table: Common Fluorophores, Lasers and Spectral Channels