Cyclic Mathematical Morphology in Polar-Logarithmic Representation

• Published in: IEEE transactions on image processing Vol. 18; no. 5; pp. 1090 - 1096
• Main Authors: Luengo-Oroz, M.A., Angulo, J.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.05.2009; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Applied sciences; Circular opening; Computational efficiency; Computer Science; Conversion; Engineering Sciences; Equivalence; Erythrocytes - cytology; Erythrocytes - pathology; Exact sciences and technology; granulometric iris code; Humans; Image converters; Image processing; Image Processing, Computer-Assisted - methods; Image texture analysis; Information, signal and communications theory; Interpolation; Iris; Iris - anatomy & histology; Mathematical analysis; Mathematical morphology; Models, Theoretical; Morphology; Pattern analysis; Pattern recognition; Pixel; polar-logarithmic coordinates; radial skeleton; red blood cell shape analysis; Representations; Shape; Signal and communications theory; Signal and Image Processing; Signal processing; Signal representation. Spectral analysis; Signal, noise; spatially variant mathematical morphology; Surface layer; Telecommunications and information theory; Texture; Geometric transformation; Grain size analysis; Logarithmic function; Polar coordinate; red blood cell shape analysis; Mathematical operator; Pattern recognition; Mathematical morphology; Texture; granulometric iris code; Image analysis; spatially variant mathematical morphology; Multiscale method; radial skeleton; Circular opening; Skeleton; polar-logarithmic coordinates; Pattern analysis; Polar-logarithmic coordinates; Red blood cell shape analysis; Spatially variant mathematical morphology; Radial skeleton; Granulometric iris code
• ISSN: 1057-7149; 1941-0042
• DOI: 10.1109/TIP.2009.2013078

We propose in this paper to perform mathematical morphology operators in a geometric transformation of an image. As a result of this procedure, processing images with regular structuring elements in the transformed domain is equivalent to working with deformed structuring elements in the original representation. More specifically, the conversion into polar-logarithmic coordinates provides satisfying results in image analysis applied to round objects, if they are roughly origin-centered. We have illustrated the interest of the derived cyclic morphology with two pattern recognition examples: erythrocyte shape analysis and multiscale description of iris textures.