Nonlinear Shape Prior from Kernel Space for Geometric Active Contours

The Geometric Active Contour (GAC) framework, which utilizes image information, has proven to be quite valuable for performing segmentation. However, the use of image information alone often leads to poor segmentation results in the presence of noise, clutter or occlusion. The introduction of shapes priors in the contour evolution proved to be an effective way to circumvent this issue. Recently, an algorithm was proposed, in which linear PCA (principal component analysis) was performed on training sets of data and the shape statistics thus obtained were used in the segmentation process. This approach was shown to convincingly capture small variations in the shape of an object. However, linear PCA assumes that the distribution underlying the variation in shapes is Gaussian. This assumption can be over-simplifying when shapes undergo complex variations. In the present work, we derive the steps for using Kernel PCA to in the GAC framework to introduce prior shape knowledge. Several experiments were performed using different training-sets of shapes. Starting with any initial contour, we show that the contour evolves to adopt a shape that is faithful to the elements of the training set. The proposed shape prior method leads to better performances than the one involving linear PCA.