Detecting Curvatures in Digital Images using Filters derived from Differential Geometry

摘要

Detection of curvature in digital images is an important theoretical and practical problem in image processing. Many important features in an image are associated with curvature and the detection of such features is reduced to detection and characterization of curvatures. Differential geometry studies many kinds of curvature operators and from these curvature operators is possible to derive powerful filters for image processing which are able to detect curvature in digital images and videos. The curvature operators are formulated in terms of partial differential operators which can be applied to images via convolution with generalized kernels derived from the the Korteweg-de Vries soliton . We present an algorithm for detection of curvature in digital images which is implemented using the Maple package ImageTools. Some experiments were performed and the results were very good. In a future research will be interesting to compare the results using the Korteweg-de Vries soliton with the results obtained using Airy derivatives. It is claimed that the resulting curvature detectors could be incorporated in standard programs for image processing.