A Bimodal Co-sparse Analysis Model for Image Processing

Abstract

The success of many computer vision tasks lies in the ability to exploit the interdependency between different image modalities such as intensity and depth. Fusing corresponding information can be achieved on several levels, and one promising approach is the integration at a low level. Moreover, sparse signal models have successfully been used in many vision applications. Within this area of research, the socalled co-sparse analysis model has attracted considerably less attention than its well-known counterpart, the sparse synthesis model, although it has been proven to be very useful in various image processing applications.In this paper, we propose a co-sparse analysis model that is able to capture the interdependency of two image modalities. It is based on the assumption that a pair of analysis operators exists, so that the co-supports of the corresponding bimodal image structures are correlated. We propose an algorithm that is able to learn such a coupled pair of operators from registered and noise-free training data. Furthermore, we explain how this model can be applied to solve linear inverse problems in image processing and how it can be used for image registration tasks. This paper extends the work of some of the authors by two major contributions. Firstly, a modification of the learning process is proposed that a priori guarantees unit norm and zero-mean of the rows of the operator. This accounts for the intuition that contrast in image modalities carries the most information. Secondly, the model is used in a novel bimodal image registration algorithm which estimates the transformation parameters of unregistered images of different modalities.

Model-Based Learning of Local Image Features for Unsupervised Texture Segmentation

“…For the relaxed learning stage, we employ a smooth (yet non-convex) approximation of the cost function. To minimize this cost function, we adapted a geometric conjugate gradient descent method proposed in [30,31] such that it fits with the proposed model. For the segmentation stage, we employ the Lagrange formulation of the piecewise constant Mumford-Shah model.…”

“…which is a good approximation of the jump penalty with equality in the limit of its parameter ν, cf. [31]. Further, we let ε = 0 in Eq.…”

“…We note that a minimum of that function is clearly achieved if the filters are orthogonal to each other, i.e., if the filter set lies in the corresponding Stiefel manifold. However, in the context of sparse coding, imposing such orthogonality directly as a hard constraint has turned out to be too restrictive, see for instance [30,31]. It is clearly visible that the effective support sizes of many filters in (a) are in fact much smaller than 9×9, and that some shifted versions of the same filter can be identified among all filters.…”

“…For a general introduction to gradient methods on matrix manifolds, we refer to [36]. The approach of [30,31] consists of a geometric variant of the conjugate gradients method with backtracking line-search and an Armijo stepsize rule. For a detailed explanation, we refer the reader to the aforementioned references.…”

Quantitative analysis for image segmentation by granular computing clustering from the view of set

“…The goal of segmentation is to simplify and/or change the representation of an image into something that is more meaningful and easier to analyze. 1 Image segmentation is typically used to locate objects and boundaries in images. More precisely, image segmentation is the process of assigning a label to every pixel in an image such that pixels with the same label share certain visual characteristics.…”