Digital Straight Lines and Convexity of Digital Regions

It is shown that a digital region is convex if and only if every pair of points in the region is connected by a digital straight line segment contained in the region. The midpoint property is shown to be a necessary but not a sufficient condition for the convexity of digital regions. However, it is shown that a digital region is convex if and only if it has the median-point property.

[1]  L. Hodes.  Discrete Approximation of Continuous Convex Blobs , 1970 .

[2]  Azriel Rosenfeld,et al.  Arcs and Curves in Digital Pictures , 1973, JACM.

[3]  Magdy Gaafar.  Convexity Verification, Block-Chords, and Digital Straight Lines , 1977 .

[4]  C. Arcelli,et al.  Regular Arcs in Digital Contours , 1975 .

[5]  Chul E. Kim.  On the Cellular Convexity of Complexes , 1981, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[6]  Azriel Rosenfeld,et al.  Parallel Computation of Contour Properties , 1981, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[7]  Azriel Rosenfeld,et al.  Connectivity in Digital Pictures , 1970, JACM.

[8]  Jack Sklansky,et al.  Minimum-Perimeter Polygons of Digitized Silhouettes , 1972, IEEE Transactions on Computers.

[9]  Jack Sklansky,et al.  Recognition of convex blobs , 1970, Pattern Recognit..

[10]  Luigi P. Cordella,et al.  Parallel Detection of Concavities in Cellular Blobs , 1976, IEEE Transactions on Computers.

[11]  Ugo Montanari.  On Limit Properties in Digitization Schemes , 1970, JACM.

[12]  AZRIEL ROSENFELD,et al.  Digital Straight Line Segments , 1974, IEEE Transactions on Computers.