A Computationally Efficient Non-Interpolation Virtual Trellis Approach for Mammogram Gradient-based Patterns Analysis

Shahid Rasheed; Muhammad Rashid; Seifedine Kadry; Salman A. AlQahtani

cs.CVOct 25, 2026

A Computationally Efficient Non-Interpolation Virtual Trellis Approach for Mammogram Gradient-based Patterns Analysis

Authors: Shahid Rasheed, Muhammad Rashid, Seifedine Kadry, Salman A. AlQahtani

Organizations: School of Information Technology, Deakin University, Australia · Department of Computer Science, University of Turin, Italy · Department of Applied Data Science, Noroff University College, Norway · Department of Computer Engineering, King Saud University, Saudi Arabia

Abstract

Feature analysis is a crucial step in medical image analysis, particularly in breast cancer classification. Traditional image analysis methods often struggle with optimal patterns along the diagonal axis, computational efficiency and feature buffer storage. Different classical operators require high-efficiency hardware for the complex operations, such as image convolution and gradient analysis, which are used for processing complex machine learning models for training and test operations. Here, in this research, we introduce a non-interpolation virtual trellis-based (NVHT) operator that utilizes a filter kernel over the same square image without transformation to a hexagonal trellis. This proposed method is very efficient in reducing computational and storage costs. The proposed operator is used for improved feature extraction efficiency and accuracy in disease classification. This method outperforms conventional approaches by leveraging a hexagonal pixel representation while maintaining high sensitivity in different directions with less storage.

Figures & tables

Figure 1: Breast cancer mammogram image analysis: (a) original image; (b) ringing (green arrow) /aliasing effect (red arrow) (c) square grid generating these problems during image processing.

Figure 2: Raw images collected from the CHSJ dataset at different annotations [ 32 ]

Figure 3: Classical filter-based methods used for breast cancer using different datasets

Cite	Technique	Features Extracted	Image Type	Remarks
[ 39 ]	Square-Triangle Tessellation Descriptor (STTD)	Not specified	MPEG-7-PartB, Tari-1000, Kimia’s 99	Captures shape geometry for efficient shape retrieval using a square trellis.
[ 40 ]	Discrete Wavelet Transform (DWT)	Not specified	General image datasets	Multi-resolution edge detection using frequency decomposition.
[ 41 ]	Histogram of Oriented Gradients (HOG)	$\sim$ 378 features per 64 $\times$ 128 image	Pedestrian detection datasets	Square grid cells used to compute gradient orientation histograms.
[ 42 ]	Canny Edge Detection with square grid sampling	Not specified	General image datasets	Localizes edges using intensity gradients and non-maximum suppression.

Table 1: Image intensity-based gradient effect over square trellis

Year	Image Type	Edge Detection Technique	Performance Metrics	Key Findings
[ 43 ]	Thermogram	Deep Learning	Classification accuracy	Integrated edge detection with deep learning for accurate lesion classification.
[ 44 ]	Thermogram	Morphology on Hexagonal Grid	Edge enhancement	Proposed a method for edge enhancement using morphological operations on hexagonal grids.
[ 44 ]	Mammogram	Binary Morphology	Edge detection efficiency	Demonstrated superior edge detection on hexagonal grids compared to rectangular grids.
[ 45 ]	MRI	Gabor Wavelet	Edge detection accuracy	Found that Gabor wavelets on hexagonal grids outperform rectangular grids in MRI images.

Table 2: Deep learning methods for gradient effect detection with key findings.

Figure 4: Proposed Method Block Diagram

Figure 5: Preprocessing CHSJ breast cancer dataset images

Figure 6: Proposed Virtual Trellis for pseudo virtual patterns (PVP) detection operators: (a) Sample square trellis (b) pseudo virtual pixel (PVP) generation (c) location and intensity of PVP; (d) PVP half-distance and intensity calculation from the central pixel (e) PVP replacing four neighboring pixels

Figure 7: Intensities and angle of direction gradient patterns

Figure 8: Intensities and angle of direction gradient patterns (a) x-directional gradient operator (0 ∘ - 180 ∘ ) (b) y-directional gradient operator (90 ∘ - 270 ∘ ) (c) yx-directional gradient operator (135 ∘ - 315 ∘ ), and (d) xy-directional gradient operator (45 ∘ - 215 ∘ )

Figure 9: Direction gradient patterns along different axis and angle using VHT operator, (a) Original image (b) grayscale channel (c) DGP along x-axis (d) DGP along y-axis (e) DGP along xy-axis, (f) DGPs along yx-axis, (g) combined results of DGPs along x an d y, (h) and finally, combined results of DGPs along x and y.

Figure 10: Pattens thinning using post processing (a) NIVT processed thick edges (b) NIVT post processed thin edges (c) color labeled connected edges

Figure 11: Figure 13. Comparative analysis of the traditional square trellis with the proposed NIVT on the top left and bottom of the image. (a) (c) Square trellis shows a blurry and low intensity edge with aliasing effect (b) & (c) Proposed NIVT method, represents the high intensities on the edges and better pattern visualization. (a) (d) images represent the dim and blurry edges when zoomed at 30x, and (b)(d) clearly show crisp edges and dominate over the square trellis.

Figure 12: Comparative analysis of the proposed method with different classical filters for edge pattern detection (a) NIVT edge detected (b) NIVT* (c) Robert (d) Sobel (e) Canny (f) Prewitt (g) Laplacian

Edge Operator	# of edges	EPI	Connected Edges	Entropy
Robert	$23053\pm 30$	$0.436\pm 0.041$	11	8.4
Sobel	$28915\pm 22$	$0.568\pm 0.027$	28	9.4
Canny	$23630\pm 18$	$0.415\pm 0.056$	55	6.8
Prewitt	$27919\pm 25$	$0.573\pm 0.022$	49	8.38
Laplacian	$23156\pm 10$	$0.468\pm 0.019$	10	4.74
Proposed NIVT	$29944\pm 27$	$0.999\pm 0.017$	63	5.56

Table 3: Proposed method evaluation based on parametric analysis.

Figure 13: Comparative analysis of the proposed NIVT method with other classical methods based on the number of detected edges

Figure 14: Comparative analysis of the proposed NIVT method with other classical methods based on EPI

Figure 15: Comparative analysis of the proposed NIVT method with other classical methods reflecting the effect of entropy over connected (continuous) edges

Figure 16: Classical method comparative analysis with proposed method w.r.t. boundary/edge structure zoomed visualization (a) classical and proposed methods implemented over the full image (b) 30x zoomed red-square cropped part to better understand the extracted structure from all existing methods

Image label	Transformation and processing time (ms)			Square to hex interpolation	Proposed NIVT	Diff.
	Square to hex mapping	Hexagonal processing	Hex to square reconstruction
22580098	1.40	3.4	2.0	6.80	4.016	3.984
20588046	1.80	1.23	1.80	4.83	0.999	3.831
20588190	2.40	1.99	1.78	6.15	1.001	5.149
22579730	1.10	2.01	2.22	5.31	1.202	4.108
22580098	1.34	0.98	1.45	3.77	0.890	2.880

Table 4: Computational cost analysis between the traditional method and the proposed NIVT method

Figure 17: Image processing time when implementing the square trellis-based method and NIVT method

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A Lightweight CNN Integrated Compact Convolutional Transformer for Multi-Scale Feature Learning and reducing computational complexity for breast cancer mammography image detection and classification

Md Taimur Ahad, Ainuddin Ahmed

Department of Management North South University, Dhaka, Bangladesh

Hybrid CNN-Transformer Architectures Medical Image Classification Lightweight CNNs Mammography Image Classification

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Over the years, Convolutional Neural Networks (CNNs) have demonstrated strong capability in cancer detection and classification using medical images. However, CNN-based models often struggle to capture long-range contextual dependencies. In such scenarios, integrating Compact Convolutional Transformer (CCT) architectures after the CCT layer allows CNN-extracted features to reshape into compact patch tokens using a CCT tokenizer, followed by the addition of positional embeddings to preserve spatial structure. Using 5-fold cross-validation, the model was tested on 3 sets of breast cancer mammography. With only 250,435 parameters, the model achieved 99%-100% accuracy across 3 datasets, indicating robust generalization. Explainable AI (XAI) was integrated into the model to explain the breast cancer classification process to enhance clinical trust. The results indicate that the proposed framework is suitable for computer-aided diagnosis systems, particularly in resource-constrained clinical environments. The novelty of the proposed CNN-integrated CCT overcomes the limitation of CNN's gradient degradation in the last layers by integrating convolutional tokenization with transformer-based learning. Lighter than ViT, which is effective in capturing long-range dependencies, the model has also proven efficient in breast cancer classification by capturing long-range dependencies among breast tissue regions.

Abstract

Mammography Image Classification

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