BWTO2D: Bayesian Wavelet Topology Optimization for Curvilinear Pattern Recognition in Magnetic Data

Publication

Abbassi, B., Cheng, L.-Z., Legault, M. (2025). Bayesian Wavelet Topology Optimization for Curvilinear Pattern Recognition in Magnetic Data. Geoscience Frontiers.

Authors: Bahman Abbassi, Li-Zhen Cheng, Marc Legault

Affiliation: Université du Québec en Abitibi-Témiscamingue (UQAT), QC J9X 5E4, Canada

Contact: bahman.abbassi@uqat.ca

Version: 1.1 | Language: MATLAB | Size: 565 KB

Repository: https://github.com/bahmanabbassi/BWTO2D

Abstract

We present an unsupervised framework for automated extraction and characterization of curvilinear geological patterns from magnetic data. The method integrates a Poisson kernel-based Continuous Wavelet Transform (kCWT), feature selection, and Bayesian Topology Optimization (BTO). The Poisson kCWT generates multidirectional, multiscale coefficient maps; a feature selection algorithm then identifies a compact, informative, and non-redundant subset by balancing feature saliency and dissimilarity. The selected features are processed with directional step filtering and adaptive thresholding to delineate curvilinear patterns. These patterns are transformed into graph representation and evaluated using a novel Graph Representativeness Metric (GRM), an unsupervised objective function that quantifies structural coherence without requiring ground truth. BTO systematically optimizes critical hyperparameters to maximize GRM, eliminating manual tuning. Validation against expert-digitized curvilinear patterns demonstrates strong correlation between GRM and supervised metrics, including Fᵦ score and fracture intensity P₂₁ ratio, confirming GRM's effectiveness as a proxy for detection quality. The framework is evaluated using synthetic magnetic data derived from the Widgiemooltha Dome geological model for algorithmic assessment, sensitivity analysis, and noise robustness testing, demonstrating graceful performance degradation under noise, while maintaining strong GRM–Fᵦ correlations. Application to aeromagnetic datasets from the Blake River Group (BRG) area in Abitibi Greenstone Belt (Quebec, Canada) confirms that the method supports fast, reproducible unsupervised structural mapping in complex geological settings.

Keywords: curvilinear pattern recognition · magnetic data · continuous wavelet transform · Bayesian optimization · graph topology

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Table of Contents

1. Description
2. Requirements
3. Repository Structure
4. Quick Start
5. Detailed Workflow
   • Step 1 — Define Coordinates
   • Step 2 — Load Point Data
   • Step 3 — Prepare kCWT Inputs (Auto)
   • Step 4 — Load Ground Truth (Optional)
   • Step 5 — Configure BTO Hyperparameters
   • Step 6 — Run BTO
   • Step 7 — Inspect Results
   • Step 8 — Export
6. BTO Objective Function Pipeline
7. Parameter Reference
   • Fixed Parameters
   • Optimizable Hyperparameters
   • Bayesian Optimization Settings
   • Validation Parameters
8. Display Options
9. Export Formats
10. File Descriptions
11. Data Directories
12. Troubleshooting
13. Citation
14. License

---

Description

BWTO2D is a MATLAB App Designer application that implements the unsupervised framework described in the paper above. It couples a four-stage image-processing pipeline — Poisson kernel-based Continuous Wavelet Transform (kCWT), kCWT coefficient selection and fusion, directional step filtering with adaptive thresholding, and graph-based topological representation — with MATLAB's Bayesian optimization (bayesopt) to automatically tune 10 hyperparameters, maximizing a novel Graph Representativeness Metric (GRM).

When ground-truth curvilinear patterns are available, the tool also tracks the Fᵦ score, fracture intensity P₂₁ ratio, Bhattacharyya coefficient (BC), and Jensen–Shannon divergence (JSD) across iterations, enabling post-hoc evaluation of the unsupervised GRM proxy against supervised metrics.

The accompanying data directories contain results for the two case studies presented in the paper: synthetic magnetic data from the Widgiemooltha Dome geological model (including noise robustness and sensitivity analyses) and aeromagnetic data from the Blake River Group (BRG) in the Abitibi Greenstone Belt, Quebec, Canada.

Key capabilities

• Geographic coordinate handling with automatic polygonization (shapefile or GeoTIFF)
• Poisson kCWT with Poisson Derivatives Mother Wavelet (PDMW) for multidirectional, multiscale coefficient maps
• Saliency- and dissimilarity-based kCWT coefficient selection and fusion (Algorithm 1 in the paper)
• Directional step filtering and adaptive thresholding for curvilinear pattern delineation
• Graph-based topological representation with GRM scoring (Eqs. 18–22 in the paper)
• Bayesian Topology Optimization with configurable acquisition function, exploration ratio, and stopping criteria (Eq. 23)
• Live iteration visualization (curvilinear pattern map + GRM vs Fᵦ scatter)
• Best-so-far progression gallery
• Export to CSV, GeoTIFF, and ESRI Shapefile

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Requirements

Requirement	Details
MATLAB	R2025b or later
Toolboxes	Statistics and Machine Learning Toolbox (for bayesopt), Image Processing Toolbox, Mapping Toolbox (for GeoTIFF/shapefile I/O)
OS	Windows (designed for Windows; see manuscript)
RAM	8 GB minimum; 16+ GB recommended for large grids or many kCWT scales/angles
Program size	565 KB

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Repository Structure

Codes/
├── BWTO2D.m                        # Main GUI application (App Designer)
├── Lineaments_Auto7.m              # BTO objective function (4-stage pipeline)
│
├── cwt2d.m                         # Core 2D kCWT engine (YAWTB-derived)
├── cwt2D_DerGus.m                  # kCWT — derivative of Gaussian (manual path)
├── cwt2D_DerPoisson.m              # kCWT — Poisson PDMW (manual path)
├── cwt2D_DerPoisson_BTO.m          # kCWT — Poisson PDMW (BTO path, Section 2.1)
├── dergauss2d.m                    # 2D derivative-of-Gaussian wavelet kernel
├── derpoisson2d.m                  # 2D Poisson Derivatives Mother Wavelet (PDMW)
│
├── CWTFeatureSelection.m           # kCWT coefficient selection and fusion (Algorithm 1)
├── step_Filtering.m                # Multi-angle directional step filter
├── getFaultDetection.m             # Hysteresis thresholding + morphological cleanup
├── FilterB.m                       # Scale-dependent Gaussian smoothing
├── nDstrb2D.m                      # 2D statistical distribution normalizer
│
├── calculateFbetaScore.m           # Bidirectional Fᵦ with tolerance buffer
├── calculateStructuralMetrics.m    # P₂₁, orientation, BC, JSD metrics
├── calculateAngularSimilarity.m    # Angular histogram comparison (optional)
├── estimateTolerancePreBTO.m       # Automatic tolerance estimation before BTO
├── plotGRMvsGroundTruth.m          # Post-BTO correlation plots
├── createRoseDiagrams.m            # Orientation extraction from raster
├── createRoseDiagramsFromVectors.m # Orientation extraction from vector shapes
│
├── useBHO_BestOutputs.m            # Reconstruct globals from best iteration
├── convertRasterToShape.m          # Raster lineaments → shape structure
├── plotNewColorMap0_.m             # Colored lineament overlay renderer
├── toggleGTVisibilityCallback.m    # UI callback — toggle ground truth display
├── toggleGTVisibilityForTab.m      # UI callback — per-tab ground truth toggle
├── toggleVectorLineamentsVisibility.m # UI callback — vector patterns toggle
├── toggleImageVisibility.m         # UI callback — density/raster toggle
│
├── Surf1.m                         # Feature map gallery viewer
├── Surf1_Enhanced.m                # Enhanced point-data viewer
├── Custom_csvwrite.m               # CSV exporter with numbered suffix
├── geotiff.m                       # GeoTIFF exporter
│
├── getopts.m                       # YAWTB option parser
├── getyawtbprefs.m                 # YAWTB preference reader
├── yashow.m / yashow_cwt2d.m / …   # YAWTB visualization utilities
├── yapuls.m / yapuls2.m             # YAWTB pulse grid generators
├── vect.m / sphgrid.m / …          # YAWTB numeric helpers
│
├── Data 1 Synthetic/               # Widgiemooltha Dome synthetic benchmark results
├── Data 2 Blake River/             # Blake River Group (BRG) case study results
└── README.md                       # This file

---

Quick Start

% 1. Add the Codes folder (and subfolders) to MATLAB's path
addpath(genpath('path/to/Codes'));

% 2. Launch the GUI
BWTO2D

The application opens a tabbed window with three tabs: Data Sets, Lineaments, and Export.

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Detailed Workflow

Step 1 — Define Coordinates

On the Data Sets tab, under the Coordinates panel:

1. Choose a coordinate method from the dropdown:

   • Rectangular coordinates — Load a .txt file containing [MinLon, MaxLon, MinLat, MaxLat].
   • Automatic polygonization — Load a .shp polygon or a georeferenced .tif / .tiff file. The bounding box and study-area polygon are extracted automatically.

2. Set Spacing (Arc-Seconds) — Controls the raster resolution. Smaller values produce finer grids but increase memory and computation time. Default: 1.

3. Set Data Filter — Optional Gaussian pre-filter sigma for the coordinate grid.

4. Click Polygonize to build the internal coordinate meshgrids (XI, YI) and the polygon mask (in).

Step 2 — Load Point Data

Still on the Data Sets tab, under the Data Sets panel:

1. Select an interpolation method:

   • Regular Interp — uses griddata with nearest-neighbor.
   • Scattered Interp — uses scatteredInterpolant with natural-neighbor.

2. Click Point Data and select a .csv or .xyz file with columns [X, Y, Value].

3. The data is interpolated onto the coordinate grid, normalized (nDstrb2D), filtered (FilterB), and stored in All_Data_Matrix.

4. Use Plot Data Sets (under the Display panel) to visualize the loaded data.

Step 3 — Prepare kCWT Inputs (Auto)

Switch to the Lineaments tab. In the BTO parameter panel:

1. Click Merge to prepare CWT_Input_Features_Matrix_Auto by selecting which loaded data layers to include as input for the Poisson kCWT.

Step 4 — Load Ground Truth (Optional)

Under the target-lineaments panel on the Lineaments tab:

1. Set Spacing and grid dimensions for the target layer.
2. Click Lineaments Shape File to load a shapefile of known/mapped curvilinear patterns (e.g., expert-digitized lineaments).
3. The shapefile is rasterized onto the coordinate grid and stored in All_Trg_Matrix.

This enables Fᵦ score tracking during BTO and post-optimization validation.

Step 5 — Configure BTO Hyperparameters

On the Lineaments tab, the left panel contains two groups:

Fixed Parameters (set once, not optimized)

GUI Field	Description	Typical Value
Number of Scales	kCWT scale count	10
Scale Dilation Factor	Step between consecutive scales	1.5
Line Resolution	Resize factor for feature maps before extraction	1
CWT Reduction To	Target dimensionality after kCWT coefficient selection	10
Image Filter	Gaussian sigma for pre-filtering (FilterB)	1

Hyperparameter Search Ranges (optimized by BTO)

Each field accepts a [min, max] range vector:

GUI Field	Variable	Type	Description
kCWT Filtering Ratio	WSFR	real	kCWT support scaling factor
Poisson Z	Z	real	PDMW wavelet parameter
Step Filter Width Variability	VSFW	real	Variance-based scaling of filter window
Dissimilarity	FDissimilarity	real	Feature selection dissimilarity weight
Saliency	FSaliency	real	Feature selection saliency percentile
CWT Angles	NAngles	integer	Number of kCWT angular orientations
Center / Range (w)	w	integer	Base window size for step filter
Step Filter Angles	NSFA	integer	Number of step-filter directional angles
Hysteresis Threshold	SLC	integer	Strength-level cutoff for component filtering (%)
Order	orderx	categorical	Derivative order: {0, 1}

Bayesian Optimization Settings

GUI Field	Description	Default
BTO Iterations	Maximum objective evaluations	50
Acquisition Function	Surrogate-based selection strategy	EI per Second Plus
Exploration Ratio	Explore (1.0) vs exploit (0.0) balance	0.5
Seed Points	Initial random evaluations	4
GP Active Set Size	Gaussian process approximation size	300
Max Time (min)	Wall-clock budget; 0 = unlimited	0
Deterministic Objective	If checked, suppresses noise modeling	off

Validation Parameters

GUI Field	Description	Default
Tolerance	Spatial buffer (coordinate units) for Fᵦ matching; leave empty for automatic estimation	(auto)
F-beta (β)	Weighting of recall vs precision; β < 1 emphasizes precision	0.2

Step 6 — Run BTO

Click Lineaments (Auto) to launch the optimization loop. The pipeline:

1. Clears previous state.
2. Builds the optimizableVariable search space from GUI ranges.
3. Wraps Lineaments_Auto7 as an anonymous objective for bayesopt.
4. Runs bayesopt with the configured settings.
5. Writes optimized values back to the GUI and saves BTO_Progress.xlsx.

A live figure updates each iteration showing the current curvilinear pattern map (left) and a GRM vs Fᵦ scatter plot (right).

Step 7 — Inspect Results

Use the Display dropdown on the Lineaments tab to view:

Display Option	Description
Target Lines	Ground-truth curvilinear patterns (vector overlay)
CWT (Auto)	kCWT coefficient maps from the best iteration
Selected (Auto)	Feature-selected kCWT maps
All Lineaments (Auto)	Per-feature curvilinear pattern overlays (tabbed gallery)
Step Filtering (Auto)	Average step-filter width visualization
Lineament Densities (Auto)	Convolution-based density heat map
Lineaments (Auto)	Final stacked binary curvilinear pattern map
Deep Lineaments (Auto)	Subset from features with above-average filter width
Shallow Lineaments (Auto)	Subset from features with below-average filter width
Fbeta Score (Auto)	Overlay with Fᵦ, precision, recall, structural metrics
GRM vs Ground Truth	Correlation scatter (GRM vs Fᵦ, P₂₁, BC, JSD)
BTO Progress (Auto)	Objective trace, parameter evolution, convergence plots
BTO Best So Far Lineaments (Auto)	Iteration-by-iteration gallery of best curvilinear pattern maps

Step 8 — Export

Switch to the Export tab. Select a data product via the radio buttons:

Radio Button	Outputs
Point Data	Original interpolated data
CWT (Auto)	CWT coefficient grids
Selected (Auto)	Feature-selected grids
Densities (Auto)	Lineament density map
All Lines (Auto)	All curvilinear patterns (vector)
Deep Lines (Auto)	Deep curvilinear patterns (vector)
Shallow Lines (Auto)	Shallow curvilinear patterns (vector)

Then click:

• CSV — Exports as [X, Y, Value] columns (raster) or [ID, X, Y] (vector).
• GRD — Exports as GeoTIFF (.tif) with geographic referencing.
• For vector outputs, a Shapefile (.shp) dialog appears automatically.

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BTO Objective Function Pipeline

Lineaments_Auto7.m implements the four-stage pipeline that bayesopt evaluates at each iteration. This corresponds to the methodology described in Sections 2.1–2.4 of the paper.

Input Image(s) + Hyperparameters h
        │
        ▼
┌──────────────────────────────────────┐
│  Stage 1: Poisson kCWT               │
│  Frequency-domain implementation     │
│  of Poisson kernel-based CWT         │
│  → multidirectional, multiscale      │
│    coefficient maps                  │
│  (Section 2.1)                       │
└──────────────┬───────────────────────┘
               │
               ▼
┌──────────────────────────────────────┐
│  Stage 2: kCWT Coefficient Selection │
│  and Fusion                          │
│  Saliency + dissimilarity-based      │
│  selection of compact, non-redundant │
│  feature subset                      │
│  (Section 2.2 / Algorithm 1)        │
└──────────────┬───────────────────────┘
               │
               ▼
┌──────────────────────────────────────┐
│  Stage 3: Curvilinear Pattern        │
│  Extraction                          │
│  Per selected feature:               │
│    FilterB → step_Filtering →        │
│    getFaultDetection →               │
│    component strength filter         │
│  Stack all features (OR)             │
└──────────────┬───────────────────────┘
               │
               ▼
┌──────────────────────────────────────┐
│  Stage 4: Topological Representation │
│  and Graph Representativeness        │
│  Graph construction → GRM scoring    │
│  (Section 2.3, Eq. 18)              │
│  BTO minimizes F(h) = −GRM_norm     │
│  (Section 2.4, Eq. 23)              │
└──────────────────────────────────────┘

Graph Representativeness Metric (GRM)

GRM quantifies structural uniqueness while minimizing redundancy (Eq. 18 in the paper):

[ \text{GRM} = \sum_{P=1}^{N} w_P \cdot \left(1 - \max_{\substack{Q=1 \ Q \neq P}}^{N} \text{sim}(S_P, S_Q)\right) ]

where w_P is the weight of segment P, and sim(S_P, S_Q) measures similarity between segments P and Q via a weighted combination (α₁ + α₂ + α₃ = 1) of:

• sim₁ — orientation similarity
• sim₂ — proximity similarity
• sim₃ — overlap similarity

BTO Objective

BTO explores the hyperparameter space χ to find the optimal configuration h* that maximizes the normalized GRM by minimizing (Eq. 23 in the paper):

[ \mathbf{h}^* = \arg\min_{\mathbf{h} \in \chi} F(\mathbf{h}), \quad \text{where } F(\mathbf{h}) = -\text{GRM}_{\text{norm}} ]

Since bayesopt minimizes, a more negative objective corresponds to higher GRM (better structural representativeness of extracted curvilinear patterns).

If ground truth is loaded, Fᵦ and structural metrics are computed at each iteration for tracking — they do not influence the objective.

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Parameter Reference

Fixed Parameters

Parameter	Variable	Description
Number of Scales	N_Scales	How many kCWT scales to compute. More scales capture features at more spatial frequencies.
Scale Dilation Factor	SDF	Step between scales: Scales = 1 : SDF : N_Scales×SDF.
Line Resolution	Line_Res	Image resize factor applied before curvilinear pattern extraction. 1 = original resolution.
CWT Reduction	DR	Number of kCWT feature maps retained after coefficient selection and fusion.
Image Filter Ratio	sigma2	Gaussian blur sigma applied to each feature before step filtering.

Optimizable Hyperparameters

Variable	Type	Typical Range	Role in Pipeline
WSFR	real	[0.1, 5]	kCWT support scaling factor — controls spatial extent of the mother wavelet
NAngles	integer	[2, 16]	Number of kCWT angular orientations — higher values detect more orientations but increase computation
orderx	categorical	{0, 1}	Derivative order — selects between horizontal (1,0) and vertical (0,1) emphasis
Z	real	[0.5, 10]	Poisson wavelet parameter — controls PDMW shape
w	integer	[min_w, max_w]	Base step-filter window size — larger windows detect broader/deeper features
VSFW	real	[0, 2]	Variance-based window scaling — adapts filter width per feature based on local signal variance
NSFA	integer	[2, 16]	Number of step-filter angles — directional coverage of the enhancement filter
SLC	integer	[50, 99]	Strength-level cutoff — percentile threshold for retaining connected components
FDissimilarity	real	[0, 1]	Dissimilarity weight in feature selection — higher values prefer less-correlated features
FSaliency	real	[50, 99]	Saliency percentile — edge-strength threshold during feature selection

Bayesian Optimization Settings

Setting	MATLAB Parameter	Notes
Max Evaluations	MaxObjectiveEvaluations	Total iterations including seed points
Acquisition Function	AcquisitionFunctionName	Options: expected-improvement-per-second-plus, expected-improvement, expected-improvement-plus, expected-improvement-per-second, lower-confidence-bound, probability-of-improvement
Exploration Ratio	ExplorationRatio	0 = pure exploitation, 1 = pure exploration
Seed Points	NumSeedPoints	Random initial evaluations before GP-guided search
GP Active Set	GPActiveSetSize	Subset size for scalable GP approximation
Max Time	MaxTime	Wall-clock limit in seconds (GUI input is in minutes)
Deterministic	IsObjectiveDeterministic	Set true if objective has no stochastic component

Validation Parameters

Parameter	Description
Tolerance	Spatial buffer distance (in coordinate units, e.g., arc-seconds) for matching detected curvilinear patterns to ground truth. If left empty, estimateTolerancePreBTO runs a pilot detection to find a tolerance yielding Fᵦ in [0.4, 0.6].
F-beta (β)	Controls the precision–recall trade-off. β < 1 emphasizes precision (fewer false positives); β > 1 emphasizes recall (fewer missed features). Default 0.2 strongly favors precision.

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Display Options

All display options are accessible from the Lineaments tab dropdown + Plot button:

Option	What It Shows
Target Lines	Ground-truth curvilinear patterns as vector lines over the study area with rose diagram
CWT (Auto)	Tabbed gallery of kCWT coefficient maps from the best BTO iteration
Selected (Auto)	Feature-selected kCWT maps after saliency/dissimilarity reduction
All Lineaments (Auto)	Per-feature colored curvilinear pattern overlays in a tabbed figure, each with density map, raster, and ground-truth toggles
Step Filtering (Auto)	Average adaptive step-filter width used across features
Lineament Densities (Auto)	Convolution-based density heat map of all stacked curvilinear patterns
Lineaments (Auto)	Final stacked binary curvilinear pattern map (all features combined)
Deep Lineaments (Auto)	Patterns from features whose step-filter width exceeds the average (deeper structures)
Shallow Lineaments (Auto)	Patterns from features with below-average filter width (shallower structures)
Fbeta Score (Auto)	Detected vs ground-truth overlay with Fᵦ, precision, recall, TP, FP, FN, and structural metrics
GRM vs Ground Truth	Four scatter panels: GRM vs Fᵦ, P₂₁, BC, JSD, with Pearson correlation coefficients (r)
BTO Progress (Auto)	Objective trace, minimum trace, per-variable evolution, and convergence diagnostics
BTO Best So Far Lineaments (Auto)	Iteration gallery showing the best curvilinear pattern map at each improvement step

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Export Formats

Format	Method	Content
CSV	Custom_csvwrite	Three-column [X, Y, Value] for raster products; [ID, X, Y] for vector lineaments
GeoTIFF	geotiff	Georeferenced .tif with coordinate bounds from the study area
Shapefile	shapewrite (MATLAB)	ESRI .shp + .shx + .dbf for vector curvilinear pattern geometries
Excel	Auto-generated	BTO_Progress.xlsx — full parameter trace, objective values, and convergence data per iteration

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File Descriptions

Core Application

File	Description
BWTO2D.m	Main GUI application (App Designer classdef). Contains all UI layout, callbacks, and orchestration logic.
Lineaments_Auto7.m	BTO objective function. Implements the four-stage pipeline (Poisson kCWT → kCWT coefficient selection and fusion → curvilinear pattern extraction → GRM scoring). Called by bayesopt at each iteration.

Poisson kCWT Engine

File	Description
cwt2d.m	Core 2D CWT computation engine — frequency-domain implementation (derived from YAWTB).
cwt2D_DerGus.m	kCWT with derivative-of-Gaussian kernel — used by the manual CWT path. Includes wavelet visualization.
cwt2D_DerPoisson.m	kCWT with Poisson Derivatives Mother Wavelet (PDMW) — used by the manual CWT path. Includes wavelet visualization.
cwt2D_DerPoisson_BTO.m	kCWT with PDMW — streamlined for BTO (no visualization overhead). This is the primary kernel used in the paper (Section 2.1).
dergauss2d.m	Generates the 2D derivative-of-Gaussian wavelet kernel in the frequency domain.
derpoisson2d.m	Generates the 2D Poisson Derivatives Mother Wavelet (PDMW) kernel in the frequency domain.

Image Processing

File	Description
CWTFeatureSelection.m	kCWT Coefficient Selection and Fusion — iterative selection balancing feature saliency and dissimilarity (Section 2.2 / Algorithm 1 in the paper).
step_Filtering.m	Directional step filtering — multi-angle, multi-bandwidth zero-mean step filter for curvilinear pattern enhancement (Panagiotakis and Kokinou, 2015).
getFaultDetection.m	Adaptive thresholding + morphological cleanup for binary curvilinear pattern detection.
FilterB.m	Gaussian image filter; applies imgaussfilt if sigma > 0, otherwise passes through.
nDstrb2D.m	Normalizes a 2D matrix's statistical distribution (handles NaN).
plotNewColorMap0_.m	Renders colored curvilinear pattern overlays for visualization (used in BTO path).

Validation and Metrics

File	Description
calculateFbetaScore.m	Computes Fᵦ score with configurable tolerance buffer, bidirectional matching, and length weighting.
calculateStructuralMetrics.m	Computes fracture intensity P₂₁ ratio, orientation distributions, Bhattacharyya coefficient (BC), and Jensen–Shannon divergence (JSD).
calculateAngularSimilarity.m	Angular histogram comparison between detected and target orientations (optional).
estimateTolerancePreBTO.m	Runs a quick pilot detection to auto-estimate a tolerance that yields Fᵦ ∈ [0.4, 0.6].
plotGRMvsGroundTruth.m	Generates correlation scatter plots (GRM vs each ground-truth metric).
createRoseDiagrams.m	Extracts curvilinear pattern orientations from a binary raster image.
createRoseDiagramsFromVectors.m	Extracts curvilinear pattern orientations from a vector shape structure.

Result Management and Display

File	Description
useBHO_BestOutputs.m	Reconstructs display globals (plotH1_rgb, density maps, deep/shallow splits) from stored best BTO iteration outputs.
convertRasterToShape.m	Converts a binary raster curvilinear pattern image into a MATLAB shape structure.
Surf1.m	Tabbed gallery viewer for a stack of 2D feature maps.
Surf1_Enhanced.m	Enhanced multi-panel viewer for loaded point data.
Custom_csvwrite.m	Exports a matrix to CSV with a user-specified numbered suffix.
geotiff.m	Writes a matrix as a georeferenced GeoTIFF file.

UI Toggle Callbacks

File	Description
toggleGTVisibilityCallback.m	Toggles ground-truth overlay on main figures.
toggleGTVisibilityForTab.m	Toggles ground-truth overlay per tab in the best-so-far gallery.
toggleVectorLineamentsVisibility.m	Toggles vector lineament visibility per tab.
toggleImageVisibility.m	Toggles density map or raster lineament visibility per tab.

YAWTB Library (Bundled)

Files from the Yet Another Wavelet Toolbox required by cwt2d.m:

getopts.m, getyawtbprefs.m, yashow.m, yashow_cwt2d.m, yashow_matrix.m, yashow_spheric.m, yashow_sphvf.m, yashow_timeseq.m, yashow_volume.m, yapuls.m, yapuls2.m, yapbar.m, yamax.m, yahelp.m, yadiro.m, yastrfind.m, yawopts.m, yathresh.m, vect.m, sphgrid.m, list_elem.m

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Data Directories

Directory	Contents
Data 1 Synthetic/Without Noise/	Synthetic benchmark results — Widgiemooltha Dome model, no noise (Section 3.2.1)
Data 1 Synthetic/Guassian Noise/Exp_5p/	Noise robustness test — 5% Gaussian noise (Section 3.2.3)
Data 1 Synthetic/Guassian Noise/Exp_10p/	Noise robustness test — 10% Gaussian noise (Section 3.2.3)
Data 1 Synthetic/Guassian Noise/Exp_25p/	Noise robustness test — 25% Gaussian noise (Section 3.2.3)
Data 1 Synthetic/Sensitivty/	BTO sensitivity analysis — exploration ratio, seed points, GP active set, acquisition function (Section 3.2.2)
Data 2 Blake River/Run 1–4/	Real-world case study — Blake River Group (BRG), Abitibi Greenstone Belt, Quebec (Section 4)

The synthetic data is derived from the Widgiemooltha Dome geological model (Yilgarn Craton, Western Australia) using the Noddy 3D Modelling System. The real-world data consists of aeromagnetic datasets from the volcanogenic massive sulphide-endowed Blake River Group area.

Each run directory typically contains: Data_1.csv (input), Selected_Auto_*.csv (selected features), All/Deep/Shallow Lineaments (Auto).csv (results), Lineaments Densities Auto_*.csv (density map), and a Log*.txt file.

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Troubleshooting

"Undefined function cwt2D_DerGus_BTO"

The Gaussian-kernel BTO path calls cwt2D_DerGus_BTO, which must be on your MATLAB path. The paper uses the Poisson kCWT exclusively (derpoisson2d), so this function is not needed for the default pipeline. To use Gaussian kCWT in BTO mode, create cwt2D_DerGus_BTO.m analogous to cwt2D_DerPoisson_BTO.m (stripped of visualization code from cwt2D_DerGus.m).

Out of memory during kCWT

• Reduce Number of Scales or Number of CWT Angles.
• Increase Spacing (Arc-Seconds) to coarsen the grid.
• Reduce CWT Reduction To to select fewer features.

BTO runs slowly

• Reduce BTO Iterations.
• Set a Max Time limit (in minutes).
• Use EI per Second Plus (default) as the acquisition function — it accounts for evaluation time.
• Reduce grid resolution via larger arc-second spacing.

Fᵦ is always 0 or NaN

• Verify that ground truth is loaded (click Lineaments Shape File and check the MATLAB console).
• Check that the ground-truth spacing matches the study-area grid.
• Try increasing the Tolerance value or leaving it empty for automatic estimation.

Figures do not appear

• Close any stale figures: close all in the MATLAB Command Window.
• Ensure the Lineaments tab display dropdown has a valid selection before clicking Plot.

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Citation

If you use BWTO2D in your research, please cite:

Abbassi, B., Cheng, L.-Z., Legault, M. (2025). Bayesian Wavelet Topology Optimization for Curvilinear Pattern Recognition in Magnetic Data. Geoscience Frontiers.

@article{Abbassi2025BWTO2D,
  title     = {Bayesian Wavelet Topology Optimization for Curvilinear Pattern Recognition in Magnetic Data},
  author    = {Abbassi, Bahman and Cheng, Li-Zhen and Legault, Marc},
  journal   = {Geoscience Frontiers},
  year      = {2025},
  publisher = {Elsevier}
}

Source code: https://github.com/bahmanabbassi/BWTO2D

Related work

Abbassi, B., Cheng, L.-Z. (2025). Curvilinear lineament extraction: Bayesian optimization of directional filtering, hysteresis thresholding, and graph analysis of wavelet ridge features in magnetic data. Computers & Geosciences.

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License

Copyright (c) Bahman Abbassi, Li-Zhen Cheng, Marc Legault — Université du Québec en Abitibi-Témiscamingue (UQAT). All rights reserved. This software is provided for academic and research purposes. It is licensed under the MIT License (see the LICENSE file for details) Lead Developer: Bahman Abbassi

Dependencies and Acknowledgments

This project uses components of the Yet Another Wavelet Toolbox (YAWTB), copyright (C) 2001–2002 by the YAWTB team. The original license headers have been preserved in the relevant .m files, in accordance with the YAWTB licensing conditions. YAWTB GitHub.

BWTO2D also uses:

• A geological fault detection code (hysteresis thresholding / step filtering) developed by Costas Panagiotakis: Costas Panagiotakis (2026). Detection of Geological Faults, MATLAB Central File Exchange. Retrieved March 16, 2026. Link

Note: In addition to citing BWTO2D itself, we recommend citing these packages when the corresponding modules are explicitly used.