A Non-Linear Neuron Based Detection of Isolated Pixels in Binary and Grayscale Images using Contrast Sensitive Receptive Fields

Nassir Mohammad

Source-linked AI summary

A Non-Linear Neuron Based Detection of Isolated Pixels in Binary and Grayscale Images using Contrast Sensitive Receptive Fields

Nassir Mohammad

arXiv:2609.18399v1Sep 16, 2026cs.CVcs.AI

TL;DR

Detecting single pixels that differ from their surroundings matters in image processing and can also frame anomalous nodes in spatial networks; existing approaches have limitations for grayscale images, noise, and threshold selection. The paper adapts a non-linear neuron model with spatially local excitatory and inhibitory regions to detect such anomalies without user-specified parameters. Experiments report detection in binary and artificial grayscale images, with further examples in X-ray imagery and cybersecurity.

Problem
Detecting isolated pixels matters in image applications and spatial networks, while template matching is impractical for grayscale images and derivative methods are noise-sensitive and require thresholds.
Source: §1 · p. 2, §2.2 · p. 5
Method
The method adapts a non-linear neuron model to spatially limited receptive fields, using a central excitatory region and surrounding inhibitory region for unsupervised anomaly detection.
Source: §1 · p. 2, §3 · p. 6
Results
Experiments report detection in binary and artificial grayscale images; in the cybersecurity example, the neuron model identifies all 10 rogue users without a user-specified parameter.
Source: §4 · p. 11, §5 · p. 12
Takeaways & Limitations
The paper uses isolated-pixel detection as a focused application for understanding the extension of anomaly detection to localised change detection.
Source: §5 · p. 12
The authors identify multiscale operation, larger receptive fields for clusters, and detection of lines and edges as future work.
Source: §5 · p. 12

Abstract

from arXiv · show

Identifying isolated points is important in image processing applications such as medical imaging, astronomy and quality control management. Other domains, such as cybersecurity, also present challenges that can be framed as image processing problems. One example of particular interest is the identification of anomalous single nodes in spatially organised networks where groups of nodes in different regions share similar feature values. This task can involve both binary and more complex grayscale images. However, existing methods face limitations: template matching is infeasible for grayscale images, while 2nd order derivative based methods are highly sensitive to noise and require user-specified thresholds. To overcome these issues, a novel method is proposed for detecting meaningful single-pixel deviations in images. This approach modifies and extends a neuron model, originally designed for anomaly detection, to operate on spatially diameter limited receptive fields that incorporate excitatory and inhibitory regions. The result is a method that is free from user-specified thresholds and parameters, and can be applied to both binary and grayscale images, providing an effective, robust and efficient solution.

1 Introduction

The paper focuses on detecting single pixels that differ significantly from their local surroundings, a problem with applications ranging from image inspection to spatial networks. It proposes an unsupervised, parameter-free neuron-based approach for binary and grayscale images.

1 Introduction

Image feature detection remains difficult amid noise, occlusions, and varying lighting conditions.Source: §1 · p. 2
Isolated-pixel detection targets significant deviations from local surroundings, including porous points, tiny industrial defects, and scanning or noise artifacts.The paper also frames anomalous nodes in spatially organised networks as an image-processing application.Source: §1 · p. 2
Existing template-matching and second-order derivative approaches have grayscale-image limitations, while derivative methods are sensitive to noise and require threshold tuning.The introduction identifies these approaches as established bases of feature detection.Source: §1 · p. 2
The proposed method uses non-linear neurons for unsupervised anomaly detection in spatially local receptive fields, with lateral inhibition, to detect isolated pixels in binary and grayscale images.It adapts to input data rather than measuring change with derivatives or requiring user-specified thresholds.Source: §1 · pp. 2–3

2 Prior Art

Prior art detects isolated pixels either by exact binary pattern matching or by second-order derivatives. The paper describes the scope and operating requirements of each approach, including their practical limitations.

2.1 Template Matching: the Hit or Miss Operator

The hit-or-miss transform slides a structuring element over a binary image and marks the center pixel only when the underlying values exactly match.Figure 1 shows masks for isolated foreground pixels and isolated background pixels.Source: §2.1 · p. 3, Figure 1 · p. 4
For an 8-bit 3 × 3 grayscale patch, 256^9 possible patterns make exhaustive template matching impractical.The hit-or-miss transform is constrained to binary images, where isolated pixels correspond to two fixed patterns.Source: §2.1 · p. 3

2.2 Second Order Derivatives: the Laplacian Filter

The Laplacian filter approximates second derivatives and responds to isolated pixels that differ in intensity from their surroundings.Its absolute response is compared with a threshold T to identify isolated pixels; Figure 2 depicts the Laplacian mask.Source: §2.2 · pp. 4–5, Figure 2 · p. 4
Second-order derivatives detect abrupt grayscale changes, but their sensitivity to noise and dependence on a suitable threshold can cause false positives or false negatives.A single threshold may not work consistently across images or within one image when intensity changes vary.Source: §2.2 · pp. 4–5

3 The Non-linear Neuron Detector

The detector adapts Mohammad’s non-linear anomaly-detection neuron to spatially limited image receptive fields. It tests local deviations and fires only for an anomaly in the central excitatory region without anomalies in the inhibitory surround.

3 The Non-linear Neuron Detector

The model extends Mohammad’s anomaly-detection neuron to spatially diameter-limited receptive fields, drawing on retinal excitatory and inhibitory organization.The current implementation uses 3 × 3 pixel regions.Source: §3 · pp. 5–6
For each receptive field, the computation uses the median input intensity, the sum of absolute deviations from that median, and the number of input connections.For a 3 × 3 window, the connection count is 9.Source: §3 · p. 6
A pixel is treated as anomalous when its deviation satisfies the model’s expectation test, which defines an anomaly as an unexpected occurrence that nevertheless appears.Source: §3 · p. 6
The center is excitatory and the surrounding pixels inhibitory: the neuron fires only for a central anomaly when no anomalies occur in the surround.Source: §3 · p. 6, Figure 4 · p. 7
Applying the neuron across all possible 3 × 3 image windows produces a filter response map and avoids threshold selection.Source: §3 · p. 6

4 Example Results

The examples compare the neuron detector with template matching and the Laplacian on binary and grayscale images, including industrial X-ray and user-activity data. The neuron detects all added grayscale isolated pixels without parameters, while textured X-ray imagery requires Gaussian smoothing and the network example contrasts with threshold-sensitive Laplacian results.

4 Example Results

All methods detected the isolated pixels inside binary-image borders; template matching and the Laplacian performed well, with the Laplacian using T = 0.9.The binary images make template matching feasible.Source: §4 · p. 8, Figure 5 · p. 9
The Laplacian missed some isolated pixels in the grayscale examples, while the neuron detected all 7 square-image and 9 mach-bands-image pixels without parameters.The figure also reports an unintended Laplacian response along the mach-bands image’s bottom-right edge; changing its threshold did not necessarily improve results.Source: §4 · p. 8, Figure 6 · p. 10
On the textured turbine-blade X-ray, the Laplacian detected the defect at T = 0.9, while the neuron required Gaussian 5 × 5 smoothing to avoid false positives.Source: §4 · p. 8, Figure 7 · p. 11
In the user-activity map, the Laplacian found only 2 rogue users at T = 0.9 and all 10 at T = 0.4, whereas the neuron found all without parameter tuning.The lower Laplacian threshold was sensitive to changes in rogue-user placement.Source: Figure 7 · p. 11, §4 · p. 11

5 Conclusion and future work

The neuron model frames local receptive-field responses as anomalies, using lateral inhibition rather than derivative-based change measures. Experiments report effectiveness on binary and uniform-region artificial grayscale images, plus X-ray and cybersecurity applications; multiscale operation and richer feature detection remain future work.

The method detects localized anomalies through receptive-field responses and lateral inhibition rather than first- or second-order derivatives.The neuron model adapts to input data, avoiding threshold selection for derivative outputs.Source: §5 · p. 12
The model detected isolated pixels in binary and uniform-region artificial grayscale images; template matching was impractical for grayscale, while Laplacian threshold tuning could be inconsistent.Source: §5 · p. 12
Smoothed X-ray images improved detection, and the model identified rogue nodes represented as isolated pixels amid similar-valued regions and noise.Source: §5 · p. 12
Future work targets multiscale operation, larger receptive fields for clusters, faster parallel processing, and detection of lines and edges.Source: §5 · p. 12