A parameterless scale-space approach to find meaningful modes in histograms - Application to image and spectrum segmentation

Despite a huge literature on this topic, image segmentation remains a difficult problem in the sense there does not exist a general method which works in all cases. One reason is in that the expected segmentation generally depends on the final application goal. Generally researchers focus on the development of specific algorithms according to the type of images they are processing and their final purpose (image understanding, object detection, . . . ). Different types of approaches were developed in the past which can be broadly classified into histogram based, edge based, region based and clustering (and mixes between them). If histogram methods are conceptually straightforward, they are not the most efficient but they are still widely used because of their simplicity and the few computational resources needed to perform them (this is an important criterion for computer vision applications). The idea behind such methods is that the final classes in the segmented image correspond to “meaningful” modes in an histogram built from the image characteristics. For instance, in the case of grayscale images, each class is supposed to correspond to a mode in the histogram of the gray values. Finding such modes is basically equivalent to find a set of thresholds separating the mode supports in the histogram. Several articles are available in the literature proposing histogram based segmentation algorithms. Two main philosophies can be encountered: techniques using histograms to drive a more advanced segmentation algorithm or techniques based on the segmentation of the histogram itself. For instance, we can cite the work of Chan et al. [4], where the authors compare the empirical histograms of two regions (binary segmentation) by using the Wasserstein distance in a levelset formulation. In [17], local spectral histograms (i.e obtained by using several filters) are built. The authors show that the segmentation process is equivalent to solving a linear regression problem. Based on their formalism, they also propose a method to estimate the number of classes. In [13], a mixture model for histogram data is proposed and then used to perform the final clustering (the number of clusters is chosen accordingly with some rules from the statistical learning theory). In [14], it is shown that the HSV color space is a better color representation space than the usual RGB space. The authors use k ́Means to obtain the segmentation. They also show that this space can be used to build feature histograms to perform an image retrieval task. Another approach, called