Abstract-We propose a shape-based approach to curve evolution for the segmentation of medical images containing known object types. In particular, motivated by the work of Leventon, Grimson, and Faugeras [15], we derive a parametric model for an implicit representation of the segmenting curve by applying principal component analysis to a collection of signed distance representations of the training data. The parameters of this representation are then manipulated to minimize an objective function for segmentation. The resulting algorithm is able to handle multidimensional data, can deal with topological changes of the curve, is robust to noise and initial contour placements, and is computationally efficient. At the same time, it avoids the need for point correspondences during the training phase of the algorithm. We demonstrate this technique by applying it to two medical applications; two-dimensional segmentation of cardiac magnetic resonance imaging (MRI) and three-dimensional segmentation of prostate MRI.Index Terms-Active contours, binary image alignment, cardiac MRI segmentation, curve evolution, deformable model, distance transforms, eigenshapes, implicit shape representation, medical image segmentation, parametric shape model, principal component analysis, prostate segmentation, shape prior, statistical shape model.
W e propose a model-based curve evolution technique for segmentation of images containing known object types. I n particular, motivated by the work of Leventon, Grimson, and Faugeras [4], we derive a parametric model for a n implicit representation of the segmenting curve by applying principal component analgsis to a collection of signed distance representations of the training data. The parameters of this representution are then calculated to minimize a n objective function for segmentation. W e found the resulting algorithm to be computationally eficient, able to handle multidimensional data, robust to noise and initial contour placements, while at the same time, avoiding the need f o r point correspondences during the training phasc: of the algorithm. W e demonstrate this technique by applying it to two medical applications.
We propose a best basis algorithm for signal enhancement in white Gaussian noise.The best basis search is performed in families of orthonormal bases constructed with wavelet packets or local cosine bases. We base our search for the "best" basis on a criterion of minimal reconstruction error of the underlying signal. This approach is intuitively appealing because the enhanced or estimated signal has an associated measure of performance, namely the resulting mean-square error. Previous approaches in this framework have focused on obtaining the most "compact" signal representations, which consequently contribute to effective denoising. These approaches, however, do not possess the inherent measure of performance which our algorithm provides.We first propose an estimator of the mean-square error, based on a heuristic argument and subsequently compare our simple error criterion to the Stein unbiased risk estimator. We compare the two proposed estimators by providing both qualitative and quantitative analyses of the bias term. Having two estimators of the mean-square error, we incorporate these cost functions into the search for the "best" basis, and subsequently provide a substantiating example to demonstrate their performance.
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