A Contrario Selection of Optimal Partitions for Image Segmentation

Abstract

We present a novel segmentation algorithm based on a hierarchical representation of images. The main contribution of this work is to explore the capabilities of the a contrario reasoning when applied to the segmentation problem, and to overcome the limitations of current algorithms within that framework. This exploratory approach has three main goals.Our first goal is to extend the search space of greedy merging algorithms to the set of all partitions spanned by a certain hierarchy, and to cast the segmentation as a selection problem within this space. In this way we increase the number of tested partitions and thus we potentially improve the segmentation results. In addition, this space is considerably smaller than the space of all possible partitions, thus we still keep the complexity controlled.Our second goal aims to improve the locality of region merging algorithms, which usually merge pairs of neighboring regions. In this work, we overcome this limitation by introducing a validation procedure for complete partitions, rather than for pairs of regions.The third goal is to perform an exhaustive experimental evaluation methodology in order to provide reproducible results.Finally, we embed the selection process on a statistical a contrario framework which allows us to have only one free parameter related to the desired scale.

A Review of Classic Edge Detectors

“…For this reason, most modern approaches use a multiscale approach, were edges are detected at many different scales and the optimum scale is chosen a posteriori [13,1]. This idea can be even extended to pick edges at different scales depending on the region of the image; this idea has been applied to regions [4].…”

“…We consider this work as the first step towards a complete benchmark of edge detectors, which has to be completed with a systemic quantitative analysis. Suitable frameworks for this kind of analysis are proposed in the literature [4,11,5], but this is clearly outside the scope of this work. In particular, quantitatively challenging the claims of the reviewed works will be a great contribution to the area, which is very weak with respect to experimental validation.…”

Hierarchizing graph-based image segmentation algorithms relying on region dissimilarity

“…A seminal work in that direction is the one of Guigues et al [10], which nd optimal cuts in the rst hierarchy. This work has been extended in several directions, see for example [3] and [17]. It is shown in [26] that mathematical morphology provides tools and operators to modify hierarchies, in a spirit similar to what is achieved in [10].…”

A Three-Stage Approach for Segmenting Degraded Color Images: Smoothing, Lifting and Thresholding (SLaT)

“…The paper [29] performs a simultaneous segmentation of the input image into arbitrarily many pieces using a modified version of model (1) and the final segmented image results from a stopping rule using a multigrid approach. In [17], an initial hierarchy of regions is obtained by greedy iterative region merging using model (2); the final segmentation is obtained by thresholding this hierarchy using hypothesis testing. The paper [2] first determines homogeneous regions in the noisy image with a special emphasis on topological changes; then each region is restored using model (1).…”

“…However, a study on this point in [37] shows that the Lab (perceived lightness, redgreen and yellow-blue) color space defined by the CIE (Commission Internationale de l'Eclairage) is better adapted for color image segmentation than the RGB and the HSI color spaces. In [17] RGB input images are first converted to Lab space. In [49] color features are described using the Lab color space and texture using histograms in RGB space.…”