Linear Feature Extraction with 3-D LSB-Snakes

In this paper, active contour models (Snakes) are formulated in a least squares context and extended to integrate multiple images for linear features extraction in a fully 3-D mode. This novel concept of LSB-Snakes (Least Squares B-spline Snakes) improves considerably concept and performance of active contour models by using three elements: (i) the possibility for internal quality control through computation of the covariance matrix of the estimated parameters, (ii) the exploitation of any a priori known geometric (e. g. splines for a smooth curve) and photometric information to constrain the solution and (iii) the simultaneous use of any number of images through the integration of camera models. 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 or GIS-supplied seed points. By connecting image and object space through the camera models, any number of images can be accommodated simultaneously and the solution parameters describing the linear feature can be determined directly in 3-D object space. Compared to the classical two-image approach this multi-image mode allows to control blunders, like occlusions, which may appear in some of the images, very well. The issues related to the mathematical modelling of the proposed method are discussed and experimental results related to the extraction of roads are shown too.