RECOGNITION OF COLOR IMAGES USING QUATERNION CONVOLUTIONAL NEURAL NETWORKS

Abstract

This article addresses the pressing scientific and practical problem of enhancing the parametric efficiency and robustness of computer vision systems against color and chromatic distortions by employing the framework of Hamilton quaternion algebra. Several quaternion convolutional neural network (QCNN) architectures for color image classification are proposed, and the effectiveness of the selected solutions is substantiated. A custom QConv2D convolutional layer was implemented to perform the non-commutative Hamilton product W ⊗ X within the TensorFlow/Keras 3 environment, supporting XLA compilation and the keras.ops specification. A stabilized architecture, Stable QCNN, is proposed; it combines parameterized color space embedding via Conv2D(4, 1x1), the GELU activation function, normalized quaternion weight initialization, and differential learning rates.

To validate the results, a detailed comparison of four model types was conducted: Standard CNN, Basic QCNN, Improved QCNN, and Stable QCNN. Testing was performed on three distinct datasets subjected to various types of distortions: CIFAR-10-C, SVHN with additive chromatic noise, and Oxford Flowers-102. It is demonstrated that quaternion color representation ensures greater robustness against high-frequency Gaussian noise and independent chromatic channel noise compared to scalar CNNs. Tests on the SVHN dataset at a high noise level of σ = 0.4 revealed that the scalar Standard CNN model suffered a significant accuracy loss of 71.76%. In contrast, the purely quaternionic Basic QCNN network proved far more robust, showing a performance drop of only 31.82%.

Moreover, it requires 3.4–3.6 times fewer parameters (just 0.67M versus 2.27M) and trains 4.2–4.4 times faster; for instance, a single epoch takes only 31.4 seconds instead of 138.1 seconds.

On the Oxford Flowers-102 dataset, the hybrid Improved QCNN model achieved a Top-1 accuracy of 80.34% and a Top-5 accuracy of 95.05%. The optimal balance between network depth and width was investigated to achieve maximum accuracy within limited computational constraints.

Keywords: quaternion convolutional neural networks, QCNN, Hamilton product, Keras 3, TensorFlow, computer vision, chromatic noise, CIFAR-10-C, SVHN, Oxford Flowers-102, parametric efficiency.