Shape-Driven 3D Segmentation Using Spherical Wavelets

Abstract

Abstract. This paper presents a novel active surface segmentation algorithm using a multiscale shape representation and prior. We define a parametric model of a surface using spherical wavelet functions and learn a prior probability distribution over the wavelet coefficients to model shape variations at different scales and spatial locations in a training set. Based on this representation, we derive a parametric active surface evolution using the multiscale prior coefficients as parameters for our optimization procedure to naturally include the prior in the segmentation framework. Additionally, the optimization method can be applied in a coarse-to-fine manner. We apply our algorithm to the segmentation of brain caudate nucleus, of interest in the study of schizophrenia. Our validation shows our algorithm is computationally efficient and outperforms the Active Shape Model algorithm by capturing finer shape details.

Multiscale 3-D Shape Representation and Segmentation Using Spherical Wavelets

“…To define w(n, m), we first find the sample correlation and pvalue between the random variables U n and Um (16) where is the sample mean of u n , σ U n the sample standard deviations of U n , and K is the total number of samples (number of shapes in the population).…”

“…This work addresses this gap and presents three novel contributions for shape representation, multiscale prior probability estimation, and segmentation. Finally, we should note that preliminary versions of the approach described in the present paper have appeared in the conference proceedings in [15] and [16].…”

Model-Guided Segmentation of 3D Neuroradiological Image Using Statistical Surface Wavelet Model

“…Due to the existence of edge features of surrounding objects, the objective function has many local maximals. One needs to ensure that the global maximum is close to the initial guess of the solution in order to use local optimization algorithms, such as gradient descent, direction set and conjugate gradient [8] [10][11] [3]. On the other hand, with our wavelet model, this is not much of an issue.…”

“…Our work here differs from the recent work on shapedriven segmentation using spherical wavelet [8]. Their work uses wavelets [9] defined on a triangulated subdivision mesh, and a different objective function (and multiscale gradient descent algorithm) in performing model-guided segmentation.…”

Segmenting images analytically in shape space

“…Many different methods (using both parameterized or implicit representation of shapes) have been proposed [1][2][3][4][5][6][7][8] to separate an object from the background using shape information. Many authors 3,6,7,9,10 use linear PCA to provide shape prior in their segmentation algorithms.…”