A Measure of Directional Convexity Inspired by Binary Tomography

On Orthogonal Projections on the Space of Consistent Pairwise Comparisons Matrices

“…The growing number of various orthogonalization approaches in [1,2,3,4] supports the importance of orthogonalization in various computer science applications. Pairwise comparisons allow us to express assessments of many entities (especially, of the subjective nature) into one value for the use in the decision making process.…”

Limited-view binary tomography reconstruction assisted by shape centroid

“…However, they require data from at least two or even more projection directions. In BT, the projection data is often amended by prior information of the image to be reconstructed, such as, e.g., smoothness, convexity, texture [2,33,38,40].…”

Texture, Nonogram, and Convexity Priors in Binary Tomography

“…Other methods use simplification of the contour [55] or a probabilistic approach [72,73] to solve the problem. Recently, measures based on directional (line) convexity have been defined and investigated, independently, in [9,89] and in [40,41], to use the degree of directional convexity as a shape prior in image reconstruction and segmentation. These methods cannot be extended easily to a two-dimensional convexity measure.…”

“…A different approach is to employ the concept of so-called Quadrant-convexity (Q-convexity for short) [20,21], which is inherently two-dimensional. This way, an extension of the directional convexity was presented in [9], which uses quantitative information introduced in [19]. In [6,7] a different 2D convexity measure was presented, which is based on the salient points [33,34].…”

“…In [19], the authors established that Quadrant-concavity measure ϕ extends directional convexity in [9].…”