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Shape Priors for Level Set Representations
- In ECCV
, 2002
"... Level Set Representations, the pioneering framework introduced by Osher and Sethian [14] is the most common choice for the implementation of variational frameworks in Computer Vision since it is implicit, intrinsic, parameter and topology free. However, many Computer vision applications refer to ..."
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Cited by 202 (14 self)
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Level Set Representations, the pioneering framework introduced by Osher and Sethian [14] is the most common choice for the implementation of variational frameworks in Computer Vision since it is implicit, intrinsic, parameter and topology free. However, many Computer vision applications refer to entities with physical meanings that follow a shape form with a certain degree of variability. In this paper, we propose a novel energetic form to introduce shape constraints to level set representations. This formulation exploits all advantages of these representations resulting on a very elegant approach that can deal with a large number of parametric as well as continuous transformations. Furthermore, it can be combined with existing well known level set-based segmentation approaches leading to paradigms that can deal with noisy, occluded and missing or physically corrupted data. Encouraging experimental results are obtained using synthetic and real images.
A shape-based approach to the segmentation of medical imagery using level sets
- IEEE Trans. Med. Imag
, 2003
"... 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 app ..."
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Cited by 172 (11 self)
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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. I.
A review of statistical approaches to level set segmentation: Integrating color, texture, motion and shape
- International Journal of Computer Vision
, 2007
"... Abstract. Since their introduction as a means of front propagation and their first application to edge-based segmentation in the early 90’s, level set methods have become increasingly popular as a general framework for image segmentation. In this paper, we present a survey of a specific class of reg ..."
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Cited by 169 (4 self)
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Abstract. Since their introduction as a means of front propagation and their first application to edge-based segmentation in the early 90’s, level set methods have become increasingly popular as a general framework for image segmentation. In this paper, we present a survey of a specific class of region-based level set segmentation methods and clarify how they can all be derived from a common statistical framework. Region-based segmentation schemes aim at partitioning the image domain by progressively fitting statistical models to the intensity, color, texture or motion in each of a set of regions. In contrast to edge-based schemes such as the classical Snakes, region-based methods tend to be less sensitive to noise. For typical images, the respective cost functionals tend to have less local minima which makes them particularly well-suited for local optimization methods such as the level set method. We detail a general statistical formulation for level set segmentation. Subsequently, we clarify how the integration of various low level criteria leads to a set of cost functionals and point out relations between the different segmentation schemes. In experimental results, we demonstrate how the level set function is driven to partition the image plane into domains of coherent color, texture, dynamic texture or motion. Moreover, the Bayesian formulation allows to introduce prior shape knowledge into the level set method. We briefly review a number of advances in this domain.
Automatic construction of 3D statistical deformation models using non-rigid registration
- IEEE Transactions on Medical Imaging
, 2003
"... Abstract. In this paper we introduce the concept of statistical deformation models (SDM) which allow the construction of average models of the anatomy and their variability. SDMs are build by performing a statistical analysis of the deformations required to map anatomical features in one subject int ..."
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Cited by 161 (8 self)
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Abstract. In this paper we introduce the concept of statistical deformation models (SDM) which allow the construction of average models of the anatomy and their variability. SDMs are build by performing a statistical analysis of the deformations required to map anatomical features in one subject into the corresponding features in another subject. The concept of SDMs is similar to active shape models (ASM) which capture statistical information about shapes across a population but offers several new advantages: Firstly, SDMs can be constructed directly from images such as MR or CT without the need for segmentation which is usually a prerequisite for the construction of active shape models. Instead a non-rigid registration algorithm is used to compute the deformations required to establish correspondences between the reference subject and the subjects in the population class under investigation. Secondly, SDMs allow the construction of an atlas of the average anatomy as well as its variability across a population of subjects. Finally, SDMs take the 3D nature of the underlying anatomy into account by analysing dense 3D deformation fields rather than only the 2D surface shape of anatomical structures. We demonstrate the applicability of this new framework to MR images of the brain and show results for the construction of anatomical models from 25 different subjects. 1
Diffusion snakes: introducing statistical shape knowledge into the Mumford-Shah functional
- J. OF COMPUTER VISION
, 2002
"... We present a modification of the Mumford-Shah functional and its cartoon limit which facilitates the incorporation of a statistical prior on the shape of the segmenting contour. By minimizing a single energy functional, we obtain a segmentation process which maximizes both the grey value homogeneit ..."
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Cited by 130 (16 self)
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We present a modification of the Mumford-Shah functional and its cartoon limit which facilitates the incorporation of a statistical prior on the shape of the segmenting contour. By minimizing a single energy functional, we obtain a segmentation process which maximizes both the grey value homogeneity in the separated regions and the similarity of the contour with respect to a set of training shapes. We propose a closed-form, parameter-free solution for incorporating invariance with respect to similarity transformations in the variational framework. We show segmentation results on artificial and real-world images with and without prior shape information. In the cases of noise, occlusion or strongly cluttered background the shape prior significantly improves segmentation. Finally we compare our results to those obtained by a level set implementation of geodesic active contours.
Deformotion - Deforming Motion, Shape Average and the Joint Registration and Segmentation of Images
- International Journal of Computer Vision
, 2002
"... What does it mean for a deforming object to be "moving" (see Fig. 1)? How can we separate the overall motion (a finite-dimensional group action) from the more general deformation (a di#eomorphism)? In this paper we propose a definition of motion for a deforming object and introduce a notio ..."
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Cited by 120 (18 self)
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What does it mean for a deforming object to be "moving" (see Fig. 1)? How can we separate the overall motion (a finite-dimensional group action) from the more general deformation (a di#eomorphism)? In this paper we propose a definition of motion for a deforming object and introduce a notion of "shape average" as the entity that separates the motion from the deformation. Our definition allows us to derive novel and e#cient algorithms to register non-equivalent shapes using region-based methods, and to simultaneously approximate and register structures in grey-scale images. We also extend the notion of shape average to that of a "moving average" in order to track moving and deforming objects through time.
Kernel Density Estimation and Intrinsic Alignment for Knowledge-driven Segmentation: Teaching Level Sets to Walk
- International Journal of Computer Vision
, 2004
"... We address the problem of image segmentation with statistical shape priors in the context of the level set framework. Our paper makes two contributions: Firstly, we propose to generate invariance of the shape prior to certain transformations by intrinsic registration of the evolving level set fun ..."
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Cited by 116 (16 self)
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We address the problem of image segmentation with statistical shape priors in the context of the level set framework. Our paper makes two contributions: Firstly, we propose to generate invariance of the shape prior to certain transformations by intrinsic registration of the evolving level set function. In contrast to existing approaches to invariance in the level set framework, this closed-form solution removes the need to iteratively optimize explicit pose parameters. Moreover, we will argue that the resulting shape gradient is more accurate in that it takes into account the e#ect of boundary variation on the object's pose.
Interactive Graph Cut Based Segmentation With Shape Priors
- IN CVPR, PAGES I: 755–762
, 2005
"... ... alternative to pure automatic segmentation in many applications. While automatic segmentation can be very challenging, a small amount of user input can often resolve ambiguous decisions on the part of the algorithm. In this work, we devise a graph cut algorithm for interactive segmentation which ..."
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Cited by 116 (0 self)
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... alternative to pure automatic segmentation in many applications. While automatic segmentation can be very challenging, a small amount of user input can often resolve ambiguous decisions on the part of the algorithm. In this work, we devise a graph cut algorithm for interactive segmentation which incorporates shape priors. While traditional graph cut approaches to interactive segmentation are often quite successful, they may fail in cases where there are diffuse edges, or multiple similar objects in close proximity to one another. Incorporation of shape priors within this framework mitigates these problems. Positive results on both medical and natural images are demonstrated.
Using prior shapes in geometric active contours in a variational framework
- IJCV
, 2002
"... Abstract. In this paper, we report an active contour algorithm that is capable of using prior shapes. The energy functional of the contour is modified so that the energy depends on the image gradient as well as the prior shape. The model provides the segmentation and the transformation that maps the ..."
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Cited by 113 (3 self)
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Abstract. In this paper, we report an active contour algorithm that is capable of using prior shapes. The energy functional of the contour is modified so that the energy depends on the image gradient as well as the prior shape. The model provides the segmentation and the transformation that maps the segmented contour to the prior shape. The active contour is able to find boundaries that are similar in shape to the prior, even when the entire boundary is not visible in the image (i.e., when the boundary has gaps). A level set formulation of the active contour is presented. The existence of the solution to the energy minimization is also established. We also report experimental results of the use of this contour on 2d synthetic images, ultrasound images and fMRI images. Classical active contours cannot be used in many of these images.
Dynamical statistical shape priors for level set based tracking
- IEEE Transactions on Pattern Analysis and Machine Intelligence
, 2006
"... Abstract. In recent years, researchers have proposed to introduce statistical shape knowledge into the level set method in order to cope with insufficient low-level information. While these priors were shown to drastically improve the segmentation of images or image sequences, so far the focus has b ..."
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Cited by 102 (8 self)
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Abstract. In recent years, researchers have proposed to introduce statistical shape knowledge into the level set method in order to cope with insufficient low-level information. While these priors were shown to drastically improve the segmentation of images or image sequences, so far the focus has been on statistical shape priors that are time-invariant. Yet, in the context of tracking deformable objects, it is clear that certain silhouettes may become more or less likely over time. In this paper, we tackle the challenge of learning dynamical statistical models for implicitly represented shapes. We show how these can be integrated into a segmentation process in a Bayesian framework for image sequence segmentation. Experiments demonstrate that such shape priors with memory can drastically improve the segmentation of image sequences. 1 Level Set Based Image Segmentation In 1988, Osher and Sethian [16] introduced the level set method 1 as a means to implicitly propagate boundaries C(t) in the image plane Ω ⊂ R 2 by evolving an
