This paper presents a novel analytic technique to perform shape-driven segmentation. In our approach, shapes
are represented using binary maps, and linear PCA is utilized to provide shape priors for segmentation. Intensity
based probability distributions are then employed to convert a given test volume into a binary map representation,
and a novel energy functional is proposed whose minimum can be analytically computed to obtain the desired
segmentation in the shape space. We compare the proposed method with the log-likelihood based energy to
elucidate some key differences. Our algorithm is applied to the segmentation of brain caudate nucleus and
hippocampus from MRI data, which is of interest in the study of schizophrenia and Alzheimer's disease. Our
validation (we compute the Hausdorff distance and the DICE coefficient between the automatic segmentation
and ground-truth) shows that the proposed algorithm is very fast, requires no initialization and outperforms the
log-likelihood based energy.
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.
Mercer kernels are used for a wide range of image and signal processing tasks like de-noising, clustering, discriminant
analysis etc. These algorithms construct their solutions in terms of the expansions in a high-dimensional
feature space F. However, many applications like kernel PCA (principal component analysis) can be used more
effectively if a pre-image of the projection in the feature space is available. In this paper, we propose a novel
method to reconstruct a unique approximate pre-image of a feature vector and apply it for statistical shape
analysis. We provide some experimental results to demonstrate the advantages of kernel PCA over linear PCA
for shape learning, which include, but are not limited to, ability to learn and distinguish multiple geometries of
shapes and robustness to occlusions.