Untrained object detection based on tensor-guided diffusion with energy regularization

Abstract

This paper addresses the problem of improving the accuracy of unsupervised object detection (unsupervised detection) in digital images acquired under conditions of uneven lighting and high noise levels, where the use of neural network detectors is impossible or impractical due to the lack of labeled data, computational resource constraints, or requirements for the mathematical interpretability of results. A two-stage method is proposed that combines geometric filtering based on tensor-controlled anisotropic diffusion with subsequent contour localization using classical detectors. The local geometry of the image is described by a structure tensor, whose eigenvectors direct diffusion along the contours of objects, allowing line breaks to be “stitched” together without blurring the boundaries. To stabilize the evolutionary process, the model is formulated as a problem of minimizing an energy functional with a data-conformity term, within which three alternative energy regularizes are investigated: total variation, the Perona–Malik logarithmic potential, and the nonlinear Laplacian. Comparative experiments were conducted on a series of underwater images of sunken objects with sharp variations in local illumination and additive Gaussian noise. Quality was assessed based on the dynamics of the boundary preservation index. It was found that regularization based on total variation provides the fastest noise suppression during the initial iterations but causes a “stair-step” effect and a sharp degradation of the edge preservation index during prolonged evolution; the Perona–Malik and Lipschitz constraint models reach a stable plateau. Based on the criterion of contour positioning accuracy (Pratt’s measure), the Lipschitz constraint model showed the best result among all the methods considered, including nonlocal averages and bilateral filtering. It is shown that the boundary preservation index is suitable as an indicator of the process dynamics, but not as a metric of the final detection quality. It has been proven that applying the proposed filtering before the Kenny detector allows for obtaining closed, connected object contours without false boundaries in areas of smooth brightness gradients. The method is fully deterministic, requires no training data, and is suitable for embedded computer vision systems.