Conference Paper

A Global Criterion for the Computation of Statistical Shape Model Parameters Based on Correspondence Probabilities

DOI: 10.1007/978-3-540-78640-5_56 Conference: Bildverarbeitung für die Medizin 2008, Algorithmen, Systeme, Anwendungen, Proceedings des Workshops vom 6. bis 8. April 2008 in Berlin
Source: DBLP


A fundamental problem when building a statistical shape model (SSM) is the correspondence problem. We present an approach for unstructured point sets where one-to-one correspondences are replaced by correspondence probabilities between shapes which are determined us- ing the Expectation Maximization - Iterative Closest Points registration. We propose a unified MAP framework to compute the model parameters which leads to an optimal adaption of the model to the observations. The optimization of the MAP explanation with respect to the obser- vation and the generative model parameters leads to very efficient and closed-form solutions for (almost) all parameters. Experimental results on synthetic data and brain structures as well as a performance compar- ison with a statistical shape model built on one-to-one correspondences show the efficiency and advantages of this approach.

Download full-text


Available from: Heinz Handels, Oct 05, 2015
1 Follower
7 Reads
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: Active Shape Models are a popular method for segmenting three-dimensional medical images. To obtain the required landmark correspondences, various automatic approaches have been proposed. In this work, we present an improved version of minimizing the description length (MDL) of the model. To initialize the algorithm, we describe a method to distribute landmarks on the training shapes using a conformal parameterization function. Next, we introduce a novel procedure to modify landmark positions locally without disturbing established correspondences. We employ a gradient descent optimization to minimize the MDL cost function, speeding up automatic model building by several orders of magnitude when compared to the original MDL approach. The necessary gradient information is estimated from a singular value decomposition, a more accurate technique to calculate the PCA than the commonly used eigendecomposition of the covariance matrix. Finally, we present results for several synthetic and real-world datasets demonstrating that our procedure generates models of significantly better quality in a fraction of the time needed by previous approaches.
    Information processing in medical imaging: proceedings of the ... conference 02/2005; 19:566-77. DOI:10.1007/11505730_47
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: The authors describe a general-purpose, representation-independent method for the accurate and computationally efficient registration of 3-D shapes including free-form curves and surfaces. The method handles the full six degrees of freedom and is based on the iterative closest point (ICP) algorithm, which requires only a procedure to find the closest point on a geometric entity to a given point. The ICP algorithm always converges monotonically to the nearest local minimum of a mean-square distance metric, and the rate of convergence is rapid during the first few iterations. Therefore, given an adequate set of initial rotations and translations for a particular class of objects with a certain level of `shape complexity', one can globally minimize the mean-square distance metric over all six degrees of freedom by testing each initial registration. One important application of this method is to register sensed data from unfixtured rigid objects with an ideal geometric model, prior to shape inspection. Experimental results show the capabilities of the registration algorithm on point sets, curves, and surfaces
    IEEE Transactions on Pattern Analysis and Machine Intelligence 03/1992; 14(2):239-256. DOI:10.1109/34.121791 · 5.78 Impact Factor
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: We describe a method for automatically building statistical shape models from a training set of example boundaries/surfaces. These models show considerable promise as a basis for segmenting and interpreting images. One of the drawbacks of the approach is, however, the need to establish a set of dense correspondences between all members of a set of training shapes. Often this is achieved by locating a set of "landmarks" manually on each training image, which is time consuming and subjective in two dimensions and almost impossible in three dimensions. We describe how shape models can be built automatically by posing the correspondence problem as one of finding the parameterization for each shape in the training set. We select the set of parameterizations that build the "best" model. We define "best" as that which minimizes the description length of the training set, arguing that this leads to models with good compactness, specificity and generalization ability. We show how a set of shape parameterizations can be represented and manipulated in order to build a minimum description length model. Results are given for several different training sets of two-dimensional boundaries, showing that the proposed method constructs better models than other approaches including manual landmarking-the current gold standard. We also show that the method can be extended straightforwardly to three dimensions.
    IEEE Transactions on Medical Imaging 06/2002; 21(5):525-37. DOI:10.1109/TMI.2002.1009388 · 3.39 Impact Factor
Show more