On the projection similarity in line grouping

Mitochondria structurally resemble a chain of projected line segments (Fig. 1).Our projection-based similarity is asymmetric and non-metric.Application shows detection of mitochondria of normal morphology in EM images. This paper is concerned with the grouping of elementary line segments which are comprised of pairwise projected entities. In a dynamic and densely cluttered scene we consider a feature-driven recognition of objects with predominantly linear or quasi-linear structural elements. The motivation arises from the field of biological imaging such as the detection of mitochondria in a complex subcellular environment. Subsequent line extraction operations result in a set of line segments with different lengths, density and orientations. We observe that a distinct criterion to distinguish such a salient group of line segments from the background can be formulated as Projectivity. We introduce a new similarity measure Projection-to-Distance Ratio which combines the proximity and the amount of spanned orthogonal projections between two line segments. Further, we perform investigations on the Euclidean properties of the proposed similarity measure. We construct the similarity matrix and show that it translates into an indefinite pseudo-covariance matrix. In order to test the introduced similarity measure we examine the applicability of NN (nearest neighbor) and non-NN clustering methods for the grouping of line segments.