The segmentation of plant roots from soil and other growing media in X-ray computed tomography images is needed to effectively study the root system architecture without excavation. However, segmentation is a challenging problem in this context because the root and non-root regions share similar features. In this paper, we describe a method based on level sets and specifically adapted for this segmentation problem. In particular, we deal with the issues of using a level sets approach on large image volumes for root segmentation, and track active regions of the front using an occupancy grid. This method allows for straightforward modifications to a narrow-band algorithm such that excessive forward and backward movements of the front can be avoided, distance map computations in a narrow band context can be done in linear time through modification of 's distance transform algorithm, and regions of the image volume are iteratively used to estimate distributions for root versus non-root classes. Results are shown of three plant species of different maturity levels, grown in three different media. Our method compares favorably to a state-of-the-art method for root segmentation in X-ray CT image volumes.
The process in many level-set methods, per iteration, given these preliminaries can be represented roughly in four steps as shown in Algorithm . Because of the presence of @math in Equation , we use the narrow band hypothesis, and the band distance is a parameter in our method. To compute the curvature @math , we use the difference of normals method @cite_29 @cite_20 , and as in @cite_23 approximate @math because @math is the signed distance function.
@cite_29 @cite_23 @cite_20
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This paper describes a partial differential equation for denoising images. The proposed method is demonstrably superior to anisotropic diffusion (and its many variations) for denoising images that are approximately piecewise constant. The method relies on an equation that is the level-set equivalent of the anisotropic diffusion equation proposed by Perona and Malik (1990). This proposed equation has come up in the literature, but has failed to be fully utilized due to a lack of analysis and the need for a stable, accurate numerical implementation. Our analysis shows that the proposed method is more aggressive than anisotropic diffusion at enhancing and preserving edges, and is less sensitive to the edge contrast parameter. Empirical results confirm these advantages, and show that for certain classes of images, one should always prefer the proposed method over anisotropic diffusion. Much effort has been made in integrating different information in a variational framework to segment images. Recent works on curve propagation were able to incorporate stochastic information (see Paragios, N. and Deriche, R., J. Visual Commun. and Image Representation, 2002; Zhu, S. and Yuille, A., 1996) and prior knowledge on shapes (see Cremers, D. et al, 2002; Rousson M. and Paragios, N., 2002). The information inserted in these studies is most of the time extracted offline. Meanwhile, other approaches have proposed to extract region information during the segmentation process itself (see Chan, T. et al, 2000; Jehan-Besson, S. et al, 2002; Yezzi, A. et al, 1999). Following these new approaches and extending the work of Paragios and Deriche to vector-valued images, we propose an entirely variational framework to approach the segmentation problem. Both the image partition and the statistical parameters for each region are unknown. After a brief reminder on recent segmenting methods, we present a variational formulation obtained from a Bayesian model. After that, we show two different differentiations driving to the same evolution equations. Detailed studies on gray and color images of the 2-phase case follow. We finish with an application to tracking which shows the benefits of our dynamic framework.