Edge Measures Using Similarity Regions

Maneesh Kumar Singh and Narendra Ahuja

In this paper, we present a new approach to edge detection. We see edges as delineators of local, photometrically coherent clusters of pixels. We are concerned with edges at a given pair of photometric and spatial scales. We first define the Similarity Region (SR) of a pixel as the set of pixels in it's neighborhood that form a local cluster with the pixel. The SR is discovered by using an affinity measure at the given spatial and photometric scales. It follows then that the SR's for two adjacent pixels within a region will be similar and they will be different for pixels across a region boundary. This property is used to determine if there is an edge between any two pixels. SR's of a pixel pair are evaluated for similarity in two ways - by comparing their geometric properties and by comparing the affinity distributions of pixels within them. This leads to two edge operators. The first uses Normalized difference of Moments (NdM) of the two SR's, while the second uses a $\chi^2$-measure of the two affinity distributions. These edge operators are fast, they respond to local edge features like corners faithfully and they do not introduce bias or localization errors for images with ESNR (Edge Strength to Noise Ratio) greater than 10 dB. For higher noise, the methods respond to edges of regions formed by noise. For robustness, we propose a preprocessing step that clusters data. To this end, we present two clustering algorithms based on cost function optimization. The first algorithm is an Iterated Mode algorithm that uses the histogram of pixel values in a local window to replace each pixel value with a value that has higher probability of occurrence at that pixel. The second algorithm minimizes a Soft Clustering Evaluation Function (SCEF) to partition the image into clusters such that the mutual information between these clusters is minimized. This work is closely related to Rosenfeld et al.'s iterative smoothing algorithms, histogram-based techniques and pyramid linking schemes; these relationships are pointed out. We present the responses of edge operators on synthetic and real images. The integration of these operators to define coherent edge detectors will be reported in the near future.

Keywords: edge detection, segmentation, clustering, affinity measures, similarity regions, moments, histogram, PDF modes.

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