Convolutional neural networks (CNNs) have been widely used in computer vision, including low-and middle-level vision problems such as contour detection and image reconstruction. In this paper, we propose a novel fractal-based CNN model for the problem of complicated curve detection, providing a geometric interpretation of CNN-based image model leveraging local fractal analysis. Utilizing the notion of local self-similarity, we develop a local fractal model for images. A curve detector is designed based on the model, consisting of an orientation-adaptive filtering process to enhance the local response along a certain orientation. This is followed by a post-processing step to preserve local invariance of the fractal dimension of image. We show the iterative framework of such an adaptive filtering process can be re-instantiated approximately via a CNN model, the nonlinear processing layer of which preserves fractal dimension approximately and the convolution layer achieves orientation enhancement. We demonstrate our fractal-based CNN model on the challenging task for detecting complicated curves from the texture-like images depicting microstructures of materials obtained by atomic force microscopy (AFM).
['Hongteng Xu', 'Junchi Yan', 'Nils Persson', 'Hongyuan Zha']
A Fractal-based CNN for Detecting Complicated Curves in AFM Images