Oblique projectors and relative forms in image morphology

Yu. P. Pyt'ev

Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 53 (2013) no. 12, pp. 2100-2122

Résumé

New mathematical methods are considered for the morphological analysis of classes of images and for comparative analysis of their forms as invariant (under image-recording conditions) carriers of information about scenes, objects, etc., and about their geometric shapes. The concepts of absolute and relative forms of classes of images and oblique projectors representing them are introduced and examined. These concepts are used to characterize morphological dependences. More specifically, the relative forms are characterized by the morphological independence index, and the absolute forms, by the morphological connectedness index. New methods based on the construction of relative forms of image classes and on the oblique projection technique are described as applied to the comparative analysis of absolute and relative forms of image classes, the morphological filtration of images, the identification of images, the determination of unknown objects in scene images, and other problems.

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