Multiresolution Image Segmentations in Graph Pyramids

”How do we bridge the representational gap between image features and coarse model features?” is the question asked by the authors of [47] when referring to several contemporary research issues. They identify the one-to-one correspondence between salient image features (pixels, edges, corners,...) and salient model features (generalized cylinders, polyhedrons, invariant models,...) as a limiting assumption that makes prototypical or generic object recognition impossible. They suggested to bridge and not to eliminate the representational gap, as it is done in the computer vision community for quite long, and to focus efforts on: i) region segmentation, ii) perceptual grouping, and iii) image abstraction. Let us take these goals as a guideline to consider multiresolution representations under the special viewpoint of segmentation and grouping. In [34] multiresolution representation is considered under the abstraction viewpoint. Wertheimer [51] has formulated the importance of wholes (Ganzen) and not of its individual elements and introduced the importance of perceptual grouping and organization in visual perception. Regions as aggregations of primitive pixels play an extremely important role in nearly every image analysis task. Their internal properties (color, texture, shape, ...) help to identify them, and their external relations (adjacency, inclusion, similarity of properties) are used to build groups of regions having a particular meaning in a more abstract context. The union of regions forming the group is again a region with both internal and external properties and relations. Low-level cue image segmentation can not and should not produce a complete final ’good’ segmentation, because there is no general ’good’ segmentation. Without prior knowledge, segmentation based on low-level cues will not be able to extract semantics in generic images. Using some similarity measures, the segmentation process results in ‘homogeneity’ regions with respect to the low-level cues. Problems emerge because i) homogeneity of low-level cues will not map to the semantics [28] and ii) the degree of homogeneity of a region is in general quantified by threshold(s) for a given measure [12]. Even though segmentation methods (including ours) that do not take the context of the image into consideration can not produce a ’good’ segmentation, they can be valuable tools in image analysis in the same sense as efficient edge detectors are. Note that efficient edge detectors do not consider the context of the image, too. Thus, the low-level coherence of brightness, color, texture or motion attributes should be used to sequentially come up with hierarchical partitions [46]. Mid and high level knowledge can be used to either confirm these groups or select some further attention. A wide range of computational vision problems could make use of segmented images, were such segmentation rely on efficient computation, e.g. motion estimation requires an appropriate region of support for finding correspondences; higher-level problems such as recognition and image indexing can also make use of segmentation results in the problem of matching. It is important for a grouping method to have the following properties [10]: