Use of power law models in detecting region of interest

Abstract

In this paper, we shall address the issue of semantic extraction of different regions of interest. The proposed approach is based on statistical methods and models inspired from linguistic analysis. Here, the models used are Zipf law and inverse Zipf law. They are used to model the frequency of appearance of the patterns contained in images as power law distributions. The use of these models allows to characterize the structural complexity of image textures. This complexity measure indicates a perceptually salient region in the image. The image is first partitioned into sub-images that are to be compared in some sense. Zipf or inverse Zipf law are applied to these sub-images and they are classified according to the characteristics of the power law models involved. The classification method consists in representing the characteristics of the Zipf and inverse Zipf model of each sub-image by a point in a representation space in which a clustering process is performed. Our method allows detection of regions of interest which are consistent with human perception, inverse Zipf law is particularly significant. This method has good performances compared to more classical detection methods. Alternatively, a neural network can be used for the classification phase.

Introduction

Automatic detection of regions of interest in images is one of the most critical problems in computer vision. For a human observer, detecting a perceptually important region in an image is a natural task which is done instantaneously, but for a machine it is far more difficult, as the machine lacks the cultural references and knowledge to identify the content of the scene. One of the causes for this difficulty is the subjective nature of the notion of region of interest (ROI). In the most general sense, a ROI, as its name suggests, is a part of the image for which the observer of the image shows interest. Of course, the interest shown by the observer in viewing the image is determined not only by the image itself, but also by the observer's own sensitivity. For a given image, different people could find different regions of interest. However, it can be said, in most cases, regions of interest generally have visually and structurally distinctive features than the rest of the image. Then some structural characteristics can be used to detect the ROI of an image without making hypotheses about the semantic content of the picture. The detection of the ROI consists in finding a region of the image which appears different from the background with respect to low-level features such as contrast, colour, region size and shape, distribution of contours or texture pattern. Different methods have been proposed to detect regions of interest in an image. Some are based on models of low-level human vision, such as the method proposed by Osberger and Maeder [1] which detects perceptually important regions on the image by building importance maps based on various visual characteristics. The method proposed by Itti et al. [2] is based on multiscale centre-surround contrast and the method presented by Syeda-Mahmood [3] uses a segmentation in homogenous colour regions. Other methods are based on different structural characteristics of the image without explicit reference to the human vision. The method proposed by Di Gesu et al. [4] uses symmetry transforms, Stentiford [5] uses dissimilarities in local neighbourhoods, Kadir and Brady [6] use a local measure of entropy to detect salient features in an image, Wang et al. [7] use a wavelet transform and Carlotto and Stein [8] use a fractal model.

In this paper, we shall use a new approach based on a statistical model which originates in linguistic analysis: Zipf law. This model proved efficient to represent the distribution of the frequencies of words in the form of a power law. It has been discovered in 1949 by Zipf [9] in written English texts, and Zipf distributions have been found in every natural language. Similar power laws have been put into evidence in different domains of human and natural sciences, such as income distribution by Pareto [10] and Gibrat [11], population of cities by Zipf [12] and Gabaix [13], distribution of biological species by Yule [14], distribution of galactic voids by Gaite and Manrubia [15], Internet traffic by Breslau et al. [16] and Huberman et al. [17] and in the structure of music by Manaris et al. [18] and of natural noises by Dellandrea et al. [19]. In the domain of digital images, Zipf law has been used by Vincent et al. [20] to evaluate the distortion of compressed images and by Caron et al. [21] to detect artificial objects in natural environments. The method described in this paper aims to detect the regions of interest in various digital images. A potential application is automatic determination of the ROI for JPEG2000 compression. Some restrictive constrains have been assumed so that a process is possible. We assume the ROI to be detected is a single connected region in the image. The ROI must both have a significant size and appear different from the background with respect to its structural complexity. Most often, the ROI is belonging to the foreground of the scene and contains more details than the background but our method also handles the case when the ROI is more uniform than the background.

The power law model will first be recalled, and then we will present the adaptation that is needed to apply it to image analysis. Then, the detection methods based on Zipf and inverse Zipf laws will be presented, and the influence of initial image segmentation will be discussed.