A transform for multiscale image segmentation by integrated edge and region detection

This paper describes a new transform to extract image regions at all geometric and photometric scales. It is argued that linear approaches such as convolution and matching have the fundamental shortcoming that they require a priori models of region shape. The proposed transform avoids this limitation by letting the structure emerge bottom-up from interactions among pixels in analogy with statistical mechanics and particle physics. The transform involves global computations on pairs of pixels followed by vector integration of the results rather than scalar and local linear processing. An attraction force field is computed over the image in which pixels belonging to the same region are mutually attracted and the region is characterized by a convergent flow. It is shown that the transform possesses properties that allow multiscale segmentation or extraction of original unblurred structure at all different geometric and photometric scales present in the image. This is in contrast with much of the previous work wherein multiscale structure is viewed as the smoothed structure in a multiscale decimation of image signal. Scale is an integral parameter of the force computation and the number and values of scale parameters associated with the image can be estimated automatically. Regions are detected at all a priori unknown scales resulting in automatic construction of a segmentation tree in which each pixel is annotated with descriptions of all the regions it belongs to. Although some of the analytical properties of the transform are presented for piecewise constant images it is shown that the results hold for more general images e.g. those containing noise and shading. Thus the proposed method is intended as a solution to the problem of multiscale integrated edgo and region detection or low-level image segmentation. Experimental results with synthetic and real images are given to demonstrate the properties and segmentation performance of the transform.