Scale Space Smoothing, Image Feature Extraction and Bessel Filters

The Green function of Mumford-Shah functional in the absence of discontinuities is known to be a modified Bessel function of the second kind and zero degree. Such a Bessel function is regularized here and used as a filter for feature extraction. It is demonstrated in this paper that a Bessel filter does not follow the scale space smoothing property of bounded linear filters such as Gaussian filters. The features extracted by the Bessel filter are therefore scale invariant. Edges, blobs, and junctions are features considered here to show that the extracted features remain unchanged by varying the scale of a Bessel filter. The scale invariance property of Bessel filters for edges is analytically proved here. We conjecture that Bessel filters also enjoy this scale invariance property for other kinds of features. The experimental results presente

Dynamic Steerable Blocks in Deep Residual Networks

Filters in convolutional networks are typically parameterized in a pixel basis, that does not take prior knowledge about the visual world into account. We investigate the generalized notion of frames designed with image properties in mind, as alternatives to this parametrization. We show that frame-based ResNets and Densenets can improve performance on Cifar-10+ consistently, while having additional pleasant properties like steerability. By exploiting these transformation properties explicitly, we arrive at dynamic steerable blocks. They are an extension of residual blocks, that are able to seamlessly transform filters under pre-defined transformations, conditioned on the input at training and inference time. Dynamic steerable blocks learn the degree of invariance from data and locally adapt filters, allowing them to apply a different geometrical variant of the same filter to each location of the feature map. When evaluated on the Berkeley Segmentation contour detection dataset, our approach outperforms all competing approaches that do not utilize pre-training. Our results highlight the benefits of image-based regularization to deep networks

Discrete Signal Processing on Graphs: Frequency Analysis

Signals and datasets that arise in physical and engineering applications, as well as social, genetics, biomolecular, and many other domains, are becoming increasingly larger and more complex. In contrast to traditional time and image signals, data in these domains are supported by arbitrary graphs. Signal processing on graphs extends concepts and techniques from traditional signal processing to data indexed by generic graphs. This paper studies the concepts of low and high frequencies on graphs, and low-, high-, and band-pass graph filters. In traditional signal processing, there concepts are easily defined because of a natural frequency ordering that has a physical interpretation. For signals residing on graphs, in general, there is no obvious frequency ordering. We propose a definition of total variation for graph signals that naturally leads to a frequency ordering on graphs and defines low-, high-, and band-pass graph signals and filters. We study the design of graph filters with specified frequency response, and illustrate our approach with applications to sensor malfunction detection and data classification

Weighted Mean Curvature

In image processing tasks, spatial priors are essential for robust computations, regularization, algorithmic design and Bayesian inference. In this paper, we introduce weighted mean curvature (WMC) as a novel image prior and present an efficient computation scheme for its discretization in practical image processing applications. We first demonstrate the favorable properties of WMC, such as sampling invariance, scale invariance, and contrast invariance with Gaussian noise model; and we show the relation of WMC to area regularization. We further propose an efficient computation scheme for discretized WMC, which is demonstrated herein to process over 33.2 giga-pixels/second on GPU. This scheme yields itself to a convolutional neural network representation. Finally, WMC is evaluated on synthetic and real images, showing its superiority quantitatively to total-variation and mean curvature.Comment: 12 page

Convolutional Color Constancy

Color constancy is the problem of inferring the color of the light that illuminated a scene, usually so that the illumination color can be removed. Because this problem is underconstrained, it is often solved by modeling the statistical regularities of the colors of natural objects and illumination. In contrast, in this paper we reformulate the problem of color constancy as a 2D spatial localization task in a log-chrominance space, thereby allowing us to apply techniques from object detection and structured prediction to the color constancy problem. By directly learning how to discriminate between correctly white-balanced images and poorly white-balanced images, our model is able to improve performance on standard benchmarks by nearly 40%