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Object Hierarchy in a Digital Image

The paper describes a model of binary hierarchical clustering of image pixels for object detection. In the model, a hierarchical sequence (a hierarchy) of pixel clusters is obtained adaptively to an image by iterative merging of pixel sets. Clustering of pixels depending on the number of clusters is given by a hierarchy of piecewise-constant approximations of the image and is described by a convex sequence of corresponding values of the total quadratic error, which is minimized for a given number of clusters. Due to the convexity property, the pixel clusters and their colors in the image are ordered by the absolute value of the increment of the total squared error accompanied by the dividing of cluster in two parts. For the hierarchy of pixel clusters, the problem of unambiguous assignment of image points to detected objects is formalized. In this case, the output of object detection is a sequence of object associations that incrementally reveal or disappear on a certain background. Objects are detected in accordance with the threshold value of the number of pixels in the cluster, or the threshold for the increment of the total squared error, or by other pixel cluster attributes that have a sense of a quantitative measure. The hierarchy of pixel clusters and the hierarchy of object associations are encoded with “pixel rating” stereo pair and “object rating” stereo pair. The pilot experimental results are demonstrated.