💻 computer science

Bioinspired CNNs for border completion in occluded images

This paper introduces BorderNet, a bioinspired convolutional neural network that leverages mathematical models of visual cortex border completion to significantly improve classification robustness against stripe and grid occlusions across MNIST, Fashion-MNIST, and EMNIST datasets.

Original authors: Catarina P. Coutinho, Aneeqa Merhab, Janko Petkovic, Ferdinando Zanchetta, Rita Fioresi

Published 2026-03-12

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CC BY 4.0

Original authors: Catarina P. Coutinho, Aneeqa Merhab, Janko Petkovic, Ferdinando Zanchetta, Rita Fioresi

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are looking at a familiar object, like a red apple, but someone has placed a thick, striped curtain in front of it. You can only see patches of red and green. A normal computer vision system might get confused and say, "I don't know what this is!" because the picture is broken.

However, your brain is a magician. Even with those gaps, your brain instantly "connects the dots." It fills in the missing lines and tells you, "That's definitely an apple." This ability is called border completion, and it's a superpower of the human visual cortex (the part of your brain that processes sight).

This paper is about teaching computers to do that same magic trick.

The Problem: Computers Hate Broken Pictures

The researchers started with a standard computer vision model called LeNet5. Think of LeNet5 as a very smart student who has studied thousands of pictures of numbers (like 0–9) and fashion items (like shoes and shirts). It's great at recognizing them when the picture is perfect.

But, as soon as you put a "curtain" (an occlusion) over the image—like diagonal black stripes or a grid pattern—this student gets confused. It fails to recognize the object because the critical lines are missing.

The Solution: Borrowing from Biology

The researchers asked: "How does the human brain fill in the gaps?"

They looked at the Visual Cortex (specifically a part called V1). Inside your brain, there are tiny "detectives" (neurons) that are specialized to look for lines in specific directions.

Some detectives only look for horizontal lines.
Some only look for vertical lines.
Some look for diagonal lines.

Crucially, these detectives talk to each other. If a detective sees a horizontal line on the left and another sees a horizontal line on the right, they "shake hands" (excite each other) to say, "Hey, there's probably a line connecting us!" This creates a smooth, continuous path even when the middle is missing.

The Innovation: "BorderNet"

The team built a new computer model called BorderNet. Instead of just giving the computer a blank slate to learn from scratch, they gave it a head start by installing bio-inspired filters.

Think of these filters as specialized glasses the computer wears before it even starts looking at the image.

The Old Way (LeNet5): The computer looks at the image and tries to guess the shape.
The New Way (BorderNet): Before guessing, the computer puts on four pairs of glasses: one that highlights horizontal lines, one for vertical, and two for diagonals. These glasses act like the "detectives" in the brain, actively searching for and connecting broken lines.

The Experiment: The "Occlusion Test"

To test if this worked, the researchers took three famous datasets (pictures of numbers, fashion items, and handwritten letters) and deliberately ruined them. They covered the images with:

Stripes: Like a zebra pattern blocking the view.
Grids: Like a window screen blocking the view.

They trained the computers on perfect images, but then tested them on these broken images.

The Results: The Brain Wins

The results were impressive.

When the images were slightly covered, BorderNet was much better at guessing the object than the standard model.
Even when the images were heavily covered (like 50% of the picture was black stripes), BorderNet often managed to keep its cool and identify the object, while the standard model gave up.

In simple terms, by giving the computer a "biological intuition" for how lines connect, they made it much more robust against messy, incomplete data.

Why This Matters

This isn't just about recognizing numbers better. It's a step toward making AI that is more like human vision. In the real world, cameras get dirty, objects get hidden behind people, and lighting changes. By mimicking the way our brains naturally "fill in the blanks," we can build AI systems that are less fragile and more reliable in the chaotic, imperfect real world.

The Bottom Line: The researchers took a mathematical model of how the human brain connects broken lines and used it to upgrade a computer's vision. The result? A computer that doesn't just "see" pixels, but actually "understands" shapes, even when they are partially hidden.

1. Problem Statement

The paper addresses the challenge of image classification under occlusion. In natural vision, objects are often partially hidden, yet the mammalian visual cortex (specifically the primary visual cortex, V1) possesses a robust mechanism to reconstruct missing boundaries and identify objects. Standard Convolutional Neural Networks (CNNs), however, often struggle when images are corrupted by occlusions (e.g., stripes or grids), leading to significant drops in classification accuracy. The authors aim to bridge the gap between biological contour integration mechanisms and deep learning architectures to enhance CNN robustness.

2. Methodology

A. Mathematical Modeling of Border Completion

The authors ground their approach in the mathematical modeling of the visual cortex's ability to perform border completion.

Theoretical Framework: They model V1 as a contact bundle (specifically the special Euclidean group $SE(2)$), where the state space includes spatial coordinates $(x, y)$ and orientation $\theta$ .
Sub-Riemannian Geometry: The problem of completing a contour is formulated as finding the shortest path (geodesic) in a sub-Riemannian manifold.
- A distribution $D$ is defined by vector fields $X$ (rotation) and $Y$ (translation along orientation), which are "bracket generating."
- The Hamiltonian formalism is used to derive geodesics, which represent the natural paths of contour integration.
Biological Analogy: These geodesics correspond to the "association fields" observed in neurophysiology, where neurons with collinear orientation preferences excite each other, allowing the visual system to "fill in" interrupted contours.

B. Bioinspired Architecture: BorderNet

Based on the mathematical model, the authors propose BorderNet, a modified version of the standard LeNet5 architecture.

Custom Filters: Instead of learning the initial filters from scratch, BorderNet introduces four predefined, fixed filters at the very beginning of the network.
Filter Design: These filters mimic the orientation-selective receptive fields of V1 neurons. They are $7 \times 7$ pixel kernels with a $3$-pixel wide stripe, set to value $1$ for the stripe and $0$ for the background.
Orientations: The four filters correspond to specific directions: Horizontal, Vertical, and two Diagonals.
Mechanism: These filters act as the vector field $Z$ described in the mathematical model, performing an initial orientation-aware convolution that mimics the biological process of detecting and integrating local edge directions before standard feature extraction begins.

C. Experimental Setup

Datasets: The models were tested on MNIST (digits), Fashion-MNIST (clothing), and EMNIST (extended digits).
Occlusion Types: Two types of occlusions were applied to the test sets only:
1. Stripes: Diagonal black stripes with varying width ( $w$ ) and spacing ( $s$ ).
2. Grids: Square grids composed of horizontal and vertical black stripes.
Training Protocol: Both Vanilla LeNet5 and BorderNet were trained exclusively on unoccluded (clean) images. This tests the model's ability to generalize to occluded data without explicit occlusion training.
Evaluation: The study ran 100 cycles with a fixed random seed. Performance was measured by mean accuracy, and the improvement of BorderNet over LeNet5 was calculated using bootstrapped medians (100,000 samples) with 95% confidence intervals to handle non-normal distributions.

3. Key Contributions

Theoretical Translation: Successfully translated the complex mathematical modeling of V1 border completion (sub-Riemannian geodesics) into a practical, computable CNN architecture.
Bioinspired Filter Design: Introduced a novel method of embedding fixed, orientation-selective filters into the first layer of a CNN to mimic biological contour integration, rather than relying solely on learned filters.
Robustness Validation: Demonstrated that incorporating biological priors (orientation selectivity) significantly improves CNN robustness against severe occlusions without requiring retraining on occluded data.

4. Results

The experiments compared BorderNet against the standard Vanilla LeNet5 across various occlusion severities ( $w, s \in [1, 10]$ ).

Overall Performance: BorderNet consistently outperformed LeNet5 across all three datasets (MNIST, Fashion-MNIST, EMNIST) and both occlusion types (Stripes and Grids).
Quantitative Gains:
- In many scenarios, BorderNet showed median accuracy improvements ranging from 10% to over 100% relative to the baseline LeNet5.
- For example, on EMNIST with grid occlusions of width 2 and spacing 4, BorderNet achieved an accuracy of 0.811 compared to LeNet5's 0.647 (a ~125% relative improvement).
- On Fashion-MNIST with grid occlusions (width 4, spacing 1), the improvement was 177.5%.
Severe Occlusions: While performance dropped for both models under extreme occlusion (e.g., very wide stripes), BorderNet maintained a relative advantage in most cases, though the gap narrowed when the signal was almost entirely destroyed.
Dataset Variance: The improvements were most pronounced on the more complex Fashion-MNIST and EMNIST datasets compared to the simpler MNIST, suggesting the bioinspired approach is particularly beneficial for complex textures and shapes.

5. Significance

Proof of Concept: The paper validates the hypothesis that mathematical models of the mammalian visual cortex can directly enhance the robustness of deep learning models.
Efficiency: By using fixed, predefined filters rather than training them, the approach adds minimal computational overhead while providing significant robustness gains.
Generalization: The ability to handle occlusions without training on occluded data suggests a path toward more data-efficient and generalizable AI systems that rely on structural priors (like geometry and orientation) rather than just statistical correlation.
Future Directions: The work opens avenues for integrating other biological mechanisms (e.g., lateral inhibition, specific cortical columnar structures) into CNNs to solve other vision challenges beyond occlusion.