Extraction of 3D linear features from multiple images by LSB-snakes

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Abstract
In general, the snakes or active contour models feature extraction algorithm integrates both photometric and geometric constraints, with an initial estimate of the location of the feature of interest, by an integral measure referred to as the total energy of snakes. The local minimum of this energy defines the feature of interest. To improve the stability and convergence of the solution of snakes, we propose a new implementation based on parametric B-spline approximation. Furthermore, the energies and solutions are formulated in a least squares context and extended to integrate multiple images in a fully 3-D mode. This novel concept of LSB-Snakes (least squares B-spline snakes) improves considerably active contour models by using three new elements: (1) the exploitation of any a priori known geometric (e.g. splines for a smooth curve) and photometric information to constrain the solution, (2) the simultaneous use of any number of images through the integration of camera models and (3) the possibility for internal quality control through computation of the covariance matrix of the estimated parameters. The mathematical model of LSB-snakes is formulated in terms of a combined least squares adjustment. The observation equations consist of the equations formulating the matching of a generic object model with image data, and those that express the geometric constraints and the location of operator-given seed points. By connecting image and object space through the camera models, any number of images can be simultaneously accommodated. Compared to the classical two-image approach this multi-image mode allows us to control blunders, like occlusions, which may appear in some of the images, very well. The issues related to the mathematical modeling of the proposed method are discussed and experimental results are shown in this paper.

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