Yehoshua Y. Zeevi

Samah Khawaled, Michael Zibulevsky, Yehoshua Y. Zeevi

Textural and structural features can be regraded as "two-view" feature sets. Inspired by the recent progress in multi-view learning, we propose a novel two-view classification method that models each feature set and optimizes the process of merging these views efficiently. Examples of implementation of this approach in classification of real-world data are presented, with special emphasis on medical images. We firstly decompose fully-textured images into two layers of representation, corresponding to natural stochastic textures (NST) and structural layer, respectively. The structural, edge-and-curve-type, information is mostly represented by the local spatial phase, whereas, the pure NST has random phase and is characterized by Gaussianity and self-similarity. Therefore, the NST is modeled by the 2D self-similar process, fractional Brownian motion (fBm). The Hurst parameter, characteristic of fBm, specifies the roughness or irregularity of the texture. This leads us to its estimation and implementation along other features extracted from the structure layer, to build the "two-view" features sets used in our classification scheme. A shallow neural net (NN) is exploited to execute the process of merging these feature sets, in a straightforward and efficient manner.

Samah Khawaled, Yehoshua Y. Zeevi

Self-similarity is the essence of fractal images and, as such, characterizes natural stochastic textures. This paper is concerned with the property of self-similarity in the statistical sense in the case of fully-textured images that contain both stochastic texture and structural (mostly deterministic) information. We firstly decompose a textured image into two layers corresponding to its texture and structure, and show that the layer representing the stochastic texture is characterized by random phase of uniform distribution, unlike the phase of the structured information which is coherent. The uniform distribution of the the random phase is verified by using a suitable hypothesis testing framework. We proceed by proposing two approaches to assessment of self-similarity. The first is based on patch-wise calculation of the mutual information, while the second measures the mutual information that exists across scales. Quantifying the extent of self-similarity by means of mutual information is of paramount importance in the analysis of natural stochastic textures that are encountered in medical imaging, geology, agriculture and in computer vision algorithms that are designed for application on fully-textures images.

Ido Zachevsky, Yehoshua Y. Zeevi

The Fourier magnitude has been studied extensively, but less effort has been devoted to the Fourier phase, despite its well-established importance in image representation. Global phase was shown to be more important for image representation than the magnitude, whereas local phase, exhibited in Gabor filters, has been used for analysis purposes in detecting image contours and edges. Neither global nor local phase has been modelled in closed form, suitable for Bayesian estimation. In this work, we analyze the local phase of textured images and propose a local (Markovian) model for local phase coefficients. This model is Gaussian-mixture-based, learned from the graph representation of images, based on their complex wavelet decomposition. We demonstrate the applicability of the model in restoration of images with noisy local phase and in image retrieval, where we show superior performance to the well-known hybrid input-output (HIO) method. We also provide a framework for application of the model in a general setup of image processing.