Iterative Tensor Voting for Perceptual Grouping of Ill-Defined Curvilinear Structures

Abstract

In this paper, a novel approach is proposed for perceptual grouping and localization of ill-defined curvilinear structures. Our approach builds upon the tensor voting and the iterative voting frameworks. Its efficacy lies on iterative refinements of curvilinear structures by gradually shifting from an exploratory to an exploitative mode. Such a mode shifting is achieved by reducing the aperture of the tensor voting fields, which is shown to improve curve grouping and inference by enhancing the concentration of the votes over promising, salient structures. The proposed technique is applied to delineation of adherens junctions imaged through fluorescence microscopy. This class of membrane-bound macromolecules maintains tissue structural integrity and cell-cell interactions. Visually, it exhibits fibrous patterns that may be diffused, punctate and frequently perceptual. Besides the application to real data, the proposed method is compared to prior methods on synthetic and annotated real data, showing high precision rates.

Filling Large Discontinuities in 3D Vascular Networks Using Skeleton- and Intensity-Based Information

“…The saliency map is a measure for this agreement by quantifying the degree to which votes from different segments at a given point agree on a preferential direction. As in [4,11,7], each point of T can be decomposed into eigenvectors and eigenvalues, which describe the principal directions of T and their strength at each point p:…”

“…This approach, however, only makes use of the skeleton of segmented structures. Another tensor voting strategy was proposed in [7] to segment noisy tubular structures in an iterative fashion. However, this only applies to relatively small gaps.…”

Adaptation of Tensor Voting to Image Structure Estimation

“…First, the tensorized gradient, ∇u∇u T , is used to initialize a tensor at every pixel. It is important to remark that other types of tensor can be used in the initialization step, for example, ball tensors as proposed in [23]. However, the advantage of initializing the tensors with the tensorized gradient is that the input of the structure tensor and tensor voting is the same, easing the comparison between both methods.…”

“…The accuracy of the edges extracted from the structure tensor is also good in regions far away from corners, but it is largely degraded in regions close to corners. Moreover, the method proposed by Loss et al [23] has been implemented in order to compare two different approaches for extending tensor voting to gray-scale images. Figure 12 shows the results of applying this method to the images of Figures 10a and 10e.…”

“…Unfortunately, discriminating edges from corners is not possible by applying this strategy, since both types of structure will yield high curveness using this approach. Second, Loss et al [23] initialize the tensors with ball tensors (cf. Section 2) whose size depends on the gray-scale value of the pixel.…”