Directional Morphological Filtering
IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE, VOL. 23, NO. 11, NOVEMBER 2001 1313 Directional Morphological Filtering Pierre Soille and Hugues Talbot AbstractÐWe show that a translation invariant implementation of min/max filters along a line segment of slope in the form of an irreducible fraction dy=dx can be achieved at the cost of 2 k min/max comparisons per image pixel, where k max jdxj; jdyj. Therefore, for a given slope, the computation time is constant and independent of the length of the line segment. We then present the notion of periodic moving histogram algorithm. This allows for a similar performance to be achieved in the more general case of rank filters and rank-based morphological filters. Applications to the filtering of thin nets and computation of both granulometries and orientation fields are detailed. Finally, two extensions are developed. The first deals with the decomposition of discrete disks and arbitrarily oriented discrete rectangles, while the second concerns min/max filters along gray tone periodic line segments. Index TermsÐImage analysis, mathematical morphology, rank filters, directional filters, periodic line, discrete geometry, granulometry, orientation field, radial decomposition. æ 1INTRODUCTION IMILAR to the perception of the orientation of line Section 3. Performance evaluation and comparison with Ssegments by the human brain [1], [2], computer image other approaches are carried out in Section 4. Applications processing of oriented image structures often requires a to the filtering of thin networks and the computation of bank of directional filters or template masks, each being linear granulometries and orientation fields are presented sensitive to a specific range of orientations [3], [4], [5], [6], in Section 5.
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