Digital image processing (2nd ed.)
Digital image processing (2nd ed.)
Glossary of computer vision terms
Pattern Recognition
Alternative area-perimeter ratios for measurement of 2D shape compactness of habitats
Applied Mathematics and Computation
Computer Vision
A rectilinearity measurement for 3d meshes
MIR '08 Proceedings of the 1st ACM international conference on Multimedia information retrieval
A Hu moment invariant as a shape circularity measure
Pattern Recognition
Measuring Cubeness of 3D Shapes
CIARP '09 Proceedings of the 14th Iberoamerican Conference on Pattern Recognition: Progress in Pattern Recognition, Image Analysis, Computer Vision, and Applications
International Journal of Computer Vision
Computation of the Euler number using the contact perimeter
Computers & Mathematics with Applications
Tunable cubeness measures for 3D shapes
Pattern Recognition Letters
A real-time assessment of the ship design complexity
Computer-Aided Design
Occlusion cues for image scene layering
Computer Vision and Image Understanding
Computer Methods and Programs in Biomedicine
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An easy measure of compactness for 2D (two dimensional) and 3D (three dimensional) shapes composed of pixels and voxels, respectively, is presented. The work proposed here is based on the two previous works of the measure of discrete compactness [E. Bribiesca, Measuring 2-D shape compactness using the contact perimeter, Comput. Math. Appl. 33 (1997) 1-9; E. Bribiesca, A measure of compactness for 3D shapes, Comput. Math. Appl. 40 (2000) 1275-1284]. The measure of compactness proposed here improves and simplifies the previous measure of discrete compactness. Now, using this proposed measure of compactness, it is possible to compute measures for any kind of object including porous and fragmented objects. Also, the computation of the measures is very simple by means of the use of only one equation. The measure of compactness proposed here depends in large part on the sum of the contact perimeters of the side-connected pixels for 2D shapes or on the sum of the contact surface areas of the face-connected voxels for 3D shapes. Relations between the perimeter and the contact perimeter for 2D shapes and between the area of the surface enclosing the volume and the contact surface area, are presented. The measure presented here of compactness is invariant under translation, rotation, and scaling. In this work, the term of compactness does not refer to point-set topology, but is related to intrinsic properties of objects. Finally, in order to prove our measure of compactness, we calculate the measures of discrete compactness of different objects. Also, we present an important application for brain structures quantification by means of the use of the new proposed measure of discrete compactness.