Topologically invariant methods in document image analysis

Ari David Gross; Longin Jan Latecki

doi:10.1117/12.292786

20 October 1997 Topologically invariant methods in document image analysis

Ari David Gross, Longin Jan Latecki

Proceedings Volume 3168, Vision Geometry VI; (1997) https://doi.org/10.1117/12.292786
Event: Optical Science, Engineering and Instrumentation '97, 1997, San Diego, CA, United States

Abstract

One of the main tasks of digital image analysis is to recognize the properties of real objects based on their digital images. These images are obtained by some sampling device, like a CCD camera, and are represented as finite sets of points that are assigned some value in a gray-level or color scale. A fundamental question in image understanding is which features in the digital image correspond, under a given set of conditions, to certain properties of the underlying objects. In many practical applications this question is answered empirically by visually inspecting the digital images. In this paper, a mathematically comprehensive answer is presented to this question with respect to topological properties. In particular, conditions are derived relating properties of real objects to the grid size of the sampling device which guarantee that a real object and its digital image are topologically equivalent. Moreover, we prove that a topology preserving digitization must result in well-composed or strongly connected sets. Consequently, only certain local neighborhoods are realizable for such a digitization. Using the derived topological model of a well-composed digital image, we demonstrate the effectiveness of this model with respect to the digitization, thresholding, correction, and compression of digital document images.

Citation Download Citation

Ari David Gross and Longin Jan Latecki "Topologically invariant methods in document image analysis", Proc. SPIE 3168, Vision Geometry VI, (20 October 1997); https://doi.org/10.1117/12.292786

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