Dilated Divergence Based Scale-Space Representation for Curve Analysis

This study proposes the novel dilated divergence scale-space representation for multidimensional curve-like image structure analysis. In the proposed framework, image structures are modeled as curves with arbitrary thickness. The dilated divergence analyzes the structure boundaries along the curve normal space in a multi-scale fashion. The dilated divergence based detection is formulated so as to 1) sustain the disturbance introduced by neighboring objects, 2) recognize the curve normal and tangent spaces. The latter enables the innovative formulation of structure eccentricity analysis and curve tangent space-based structure motion analysis, which have been scarcely investigated in literature. The proposed method is validated using 2D, 3D and 4D images. The structure principal direction estimation accuracies, structure scale detection accuracies and detection stabilities are quantified and compared against two scale-space approaches, showing a competitive performance of the proposed approach, under the disturbance introduced by image noise and neighboring objects. Moreover, as an application example employing the dilated divergence detection responses, an automated approach is tailored for spinal cord centerline extraction. The proposed method is shown to be versatile to well suit a wide range of applications.