Image sharpening by morphological filtering

Abstract This paper introduces a class of iterative morphological image operators with applications to sharpen digitized gray-scale images. It is proved that all image operators using a concave structuring function have sharpening properties. By using a Laplacian property, we introduce the underlying partial differential equation that governs this class of iterative image operators. The parameters of the operator can be determined on the basis of an estimation of the amount of blur present in the image. For discrete implementations of the operator class it is shown that operators using a parabolic structuring function have an efficient implementation and isotropic sharpening behavior.

[1]  L. Rudin,et al.  Feature-oriented image enhancement using shock filters , 1990 .

[2]  William F. Schreiber.  Wirephoto quality improvement by unsharp masking , 1970, Pattern Recognit..

[3]  Pierre Soille,et al.  Mathematical Morphology and Its Applications to Image Processing , 1994, Computational Imaging and Vision.

[4]  Leo Dorst,et al.  Quadratic Structuring Functions in Mathematical Morphology , 1996, ISMM.

[5]  Thomas S. Huang,et al.  Image processing , 1971 .

[6]  Leo Dorst,et al.  Two Dual Representations of Morphology Based on the Parallel Normal Transport Property , 1994, ISMM.

[7]  Robert M. Haralick,et al.  Digital Step Edges from Zero Crossing of Second Directional Derivatives , 1984, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[8]  Leo Dorst,et al.  Two dual representations of mathematical morphology based on the parallel normal transport property , 1994 .

[9]  Arnold W. M. Smeulders,et al.  Image segmentation in morphological scale-space , 1994 .

[10]  Azriel Rosenfeld,et al.  Picture Processing by Computer , 1969, CSUR.

[11]  John I. Goutsias,et al.  Mathematical Morphology and its Applications to Image and Signal Processing , 2000, Computational Imaging and Vision.

[12]  Henry P. Kramer,et al.  Iterations of a non-linear transformation for enhancement of digital images , 1975, Pattern Recognit..

[13]  J. E. den Hartog.  A framework for knowledge-based map interpretation , 1995 .

[14]  F. Meyer.  Iterative image transformations for an automatic screening of cervical smears. , 1979, The journal of histochemistry and cytochemistry : official journal of the Histochemistry Society.

[15]  John F. Brenner,et al.  Local transforms for biomedical image analysis , 1980 .

[16]  Luc Florack,et al.  Image Structure , 1997, Computational Imaging and Vision.

[17]  Thomas S. Huang,et al.  Image enhancement using the median and the interquartile distance , 1984, Comput. Vis. Graph. Image Process..

[18]  Bruno Laÿ,et al.  Image Processing: A Key to Success in Industrial Applications , 1994, ISMM.

[19]  Piet W. Verbeek,et al.  Low-level image processing by max–min filters , 1988 .

[20]  Leo Dorst,et al.  Morphological signal processing and the slope transform , 1994, Signal Process..

[21]  Jean Serra,et al.  Image Analysis and Mathematical Morphology , 1983 .