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

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

arXiv:2610.34352v1cs.CVcs.LG

TL;DR

Square-trellis mammogram processing is associated with aliasing and edge-detection difficulties. The paper uses virtual pixels and optimized filters in a virtual hexagonal-trellis approach, reporting an EPI of 0.999 for NIVT.

  • Problem

    Square-grid mammogram processing is associated with aliasing and staircase effects, while traditional edge detectors have structural-accuracy and noise-handling issues.

    Source: §1 · p. 2

  • Method

    The paper proposes virtual hexagonal-trellis edge detection using virtual pixels and optimized filter kernels.

    Source: §3.3 · p. 7, §5 · pp. 18–19

  • Results

    EPI was 0.999 for NIVT, with ±0.017 variance; NIVT also performed consistently across the dataset with reasonable edge detail.

    Source: §4 · pp. 15, 17

  • Takeaways & Limitations

    The authors describe hexagonal-trellis edge detection as a promising advancement for breast-cancer lesion diagnosis, with real-time clinical processing left to future work.

    Source: §5 · p. 19

    VHT pattern variations can be thick and coincide with neighboring patterns, making the resulting image unclear.

    Source: §3.5 · p. 9

Abstract

from arXiv · show

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.

1 Introduction

Breast-cancer mammograms are represented on square grids, where aliasing and staircase effects complicate edge detection. The study proposes an optimized filter kernel with a virtual hexagonal trellis for breast-cancer image feature analysis.

1 Introduction

  • Early and accurate detection of breast-cancer lesions is described as crucial for effective treatment and improved survival.Edge detection is identified as important for segmenting and identifying abnormal growths.Source: §1 · p. 2
  • Square-grid mammography can produce aliasing and staircase effects near affected areas, while traditional edge detectors have structural-accuracy and noise-handling issues.Hexagonal-trellis edge detection is described as offering better spatial resolution and fewer aliasing artifacts.Source: §1 · p. 2
  • The study proposes an optimized filter kernel with a virtual hexagonal trellis for feature analysis in breast-cancer imaging.The selected CHSJ images are grayscale and classified as malignant or benign.Source: §1 · p. 2

2 Related Work

Prior work applies edge-detection and hybrid methods across medical-imaging modalities, with reported performance varying by method and dataset. The section also identifies conversion costs in hexagonal processing and motivates non-interpolation processing to avoid transformation-related information loss.

2 Related Work

  • Canny, Sobel, and Prewitt studies report edge-detection and classification results across ultrasound, mammography, and MRI, while LoG results concern histopathology.Reported accuracies vary by method and modality, so these examples are not a single-dataset comparison.Source: §2 · pp. 2, 4
  • The review organizes prior square-trellis breast-lesion research by publication year, image type, edge-detection technique, and performance measures.The passage identifies Tables 1 and 2 as presenting the review.Source: §2 · p. 4, Table 1 · p. 5, Table 2 · p. 5
  • The 2015–2024 chart covers hybrid edge-detection and machine-learning models, while one cited hybrid model reports 95.3% classification accuracy and remains computationally and data expensive.The review describes hexagonal frameworks as offering superior spatial resolution and uniform sampling relative to square trellises, alongside conversion hurdles.Source: §2 · p. 4, Performance Metrics · p. 6

Performance Metrics

  • The discussion motivates non-interpolation hexagonal processing to avoid information loss during image transformation while seeking lower computational cost and storage.The passage notes that conventional methods can represent gradient direction poorly and that square-to-hexagonal conversion can require computational resources and storage.Source: Performance Metrics · p. 6

3 Proposed Methodology

The methodology overlays a virtual hexagonal trellis on the square image, avoiding grid transformation while deriving directional gradient patterns for mammogram feature analysis. It preprocesses CHSJ images, generates pseudo virtual pixels, applies four directional filter stages, then thins the extracted patterns and evaluates them with image and timing metrics.

3 Proposed Methodology

  • The proposed virtual hexagonal trellis operates over the same square grid, avoiding square-to-hexagonal transformation and reducing image storage while preserving information.The paper presents this as a response to weak directional-gradient representation and the computational and storage costs of conversion and quantization.Source: §3 · p. 6

3.1 Dataset and Preprocessing

  • The CHSJ dataset contains 7,632 raw and refined mammograms from 100 subjects, and images are resized and normalized before processing.The dataset includes benign and malignant categories, with raw and refined images kept together.Source: §3.1 · p. 7, Figure 5 · p. 7

3.2 Virtual Hexagonal Trellis

  • A virtual hexagonal trellis is implemented on the Cartesian grid by redefining virtual pixels at half distance from neighboring real pixels.The approach is intended to improve edge continuity and reduce jagged boundaries without converting the image grid.Source: §3.2 · p. 7

3.3 Virtual pixel intensity and location

  • Pseudo virtual pixels receive averaged intensity from relevant neighboring and central pixels, are placed between pixels, and replace four neighboring pixels in the trellis.The figure depicts PVP generation, location and intensity, half-distance calculation, and replacement of four neighboring pixels.Source: §3.3 · p. 7, Figure 6 · p. 8

3.4 Hexagonal Filter Kernel

  • The convolutional hexagonal filter kernel applies four directional gradient stages, spanning x, y, and both diagonal axes for edge localization.The reported directional ranges are 0°–180°, 90°–270°, 45°–225°, and 135°–315°.Source: §3.4 · pp. 8–9, Figure 8 · p. 9

3.5 Implementation and Workflow

  • VHT directional patterns capture gradients across 0°–360°, while the described traditional methods extract x- and y-axis patterns only.The x-direction operator also produces a smooth scattering effect that the passage says classical filters do not collect.Source: §3.5 · p. 9

3.6 Post-processing

  • The extracted patterns can be thick and overlap, making individual patterns unclear; post-processing is used to refine them.The workflow applies Canny edge detection with thresholds 80 and 200, then thinning to reduce edges to a single pixel while maintaining topological structures.Source: §3.5 · pp. 9, 11, §3.6 · p. 11, Figure 10 · p. 11

3.7 Performance Metrics

  • The evaluation uses edge count, EPI, entropy, and computational time to compare Sobel, Robert, and Canny detectors with the proposed NIVT method.The supplied table caption identifies a parametric evaluation, but provides no result values.Source: §3.7 · p. 13, Table 3 · p. 13

4 Results and Discussion

NIVT is reported to combine strong edge preservation and connectivity with a balanced edge count, while requiring less processing time than the conventional square-to-hexagonal pipeline. The comparisons also frame edge quality as a trade-off among preservation, connectivity, and information richness.

4 Results and Discussion

  • The authors qualitatively compared NIVT with Robert, Sobel, Canny, Prewitt, and Laplacian for edge detection and boundary structure.Figure 12 presents edge-pattern comparisons, while Figure 16 shows full images and 30× zoomed crops.Source: §4 · p. 13, Figure 12 · p. 14, Figure 16 · p. 17
  • NIVT detected 29,944 edges, fewer than Canny's 53,630 but more than Sobel's 28,915 and Prewitt's 27,919, avoiding the reported under-edging of Robert and Laplacian and over-edging of Canny.The authors describe the NIVT count as balanced, with ±27 variance across images.Source: §4 · p. 13, Figure 13 · p. 15
  • NIVT achieved an EPI of 0.999 (±0.017 variance), 63 connected edges, and entropy of 5.56, with maps described as structurally continuous without excessive noise or duplication.The EPI comparison is shown in Figure 14; Figure 15 compares connected edges and entropy.Source: §4 · pp. 15, 17, Figure 14 · p. 16, Figure 15 · p. 16
  • The comparisons describe conventional operators as trading off edge richness, connectivity, and preservation, while NIVT is reported to maintain reasonable edge detail across the dataset.The connected-edge and entropy comparison is presented together in Figure 15.Source: §4 · pp. 15, 17, Figure 15 · p. 16

4.1 Computational Time Analysis

  • NIVT processing took about 1.0 ms per image versus approximately 6.8 ms for conventional processing, or 35 ms versus 207.6 ms for 30 images.The authors attribute the shorter time to fitting the virtual hexagonal trellis without interpolation; Table 4 is identified as the computational-cost comparison.Source: §4.1 · p. 18, Table 4 · p. 18

5 Conclusion and Future Work

The conclusion presents virtual hexagonal trellis edge detection with optimized filter kernels as an approach for breast cancer image analysis. It identifies deep-learning integration, real-time clinical processing, and more efficient grid conversion as future directions.

5 Conclusion and Future Work

  • The Virtual Hexagonal Trellis-Based Edge Detection method is presented as an approach to medical image analysis, particularly breast cancer detection.The authors associate optimized filter kernels and hexagonal pixel structures with edge continuity, reduced noise sensitivity, and computational efficiency.Source: §5 · pp. 18–19
  • Figure 17 compares image-processing time for the square trellis-based method and NIVT.Source: Figure 17 · p. 19
  • Future work includes integrating deep learning for automated edge refinement and developing real-time processing for clinical applications.The conclusion also calls for efficient grid-conversion algorithms and optimized computational processes to support wider adoption.Source: §5 · p. 19

Statements and Declarations

The declarations acknowledge project funding, report no conflicts of interest, and describe how processed data, code, and results may be requested.

Funding

  • The project received support from the Ongoing Research Funding program - Research Chairs (ORF-RC-2025-5300), King Saud University, Riyadh, Saudi Arabia.Source: Funding · p. 19

Competing Interests

Data and Code Availability

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