1 Bayesian Segmentation of Range Images of Polyhedral Objects using Entropy Controlled Quadratic Markov Measure Field Models (original) (raw)
Applied Optics, 2008
In this paper, a method based on Bayesian estimation with prior MRF models for segmentation of range images of polyhedral objects is presented. This method includes new ways to determine the confidence associated with the information given for every pixel in the image as well an improved method for the localization of the boundaries between regions. The performance of the method compares favorably with other state of the art procedures when evaluated using standard benchmark.
Entropy-Controlled Quadratic Markov Measure Field Models for Efficient Image Segmentation
IEEE Transactions on Image Processing, 2000
We present a new Markov Random Field (MRF) based model for parametric image segmentation. Instead of directly computing a label map, our method computes the probability that the observed data at each pixel is generated by a particular intensity model. Prior information about segmentation smoothness and low entropy of the probability distribution maps is codified in the form of a MRF with quadratic potentials, so that the optimal estimator is obtained by solving a quadratic cost function with linear constraints. Although for segmentation purposes the mode of the probability distribution at each pixel is naturally used as an optimal estimator, our method permits the use of other estimators, such as the mean or the median, which may be more appropriate for certain applications. Numerical experiments and comparisons with other published schemes are performed, using both synthetic images and real data of brain MRI for which expert hand-made segmentations are available. Finally, we show that the proposed methodology may be easily extended to other problems, such as stereo disparity estimation.
A tree-structured Markov random field model for bayesian image segmentation
IEEE Transactions on Image Processing, 2003
We present a new image segmentation algorithm based on a tree-structured binary MRF model. The image is recursively segmented in smaller and smaller regions until a stopping condition, local to each region, is met. Each elementary binary segmentation is obtained as the solution of a MAP estimation problem, with the region prior modeled as an MRF. Since only binary fields are used, and thanks to the tree structure, the algorithm is quite fast, and allows one to address the cluster validation problem in a seamless way. In addition, all field parameters are estimated locally, allowing for some spatial adaptivity.
Image segmentation based on the integration of markov random fields and deformable models
2000
This paper proposes a new methodology for image segmentation based on the integration of deformable and Markov Random Field models. Our method makes use of Markov Random Field theory to build a Gibbs Prior model of medical images with arbitrary initial parameters to estimate the boundary of organs with low signal to noise ratio (SNR). Then we use a deformable model to fit the estimated boundary. The result of the deformable model fit is used to update the Gibbs prior model parameters, such as the gradient threshold of a boundary. Based on the updated parameters we restart the Gibbs prior models. By iteratively integrating these processes we achieve an automated segmentation of the initial images. By careful choice of the method used for the Gibbs prior models, and based on the above method of integration with deformable model our segmentation solution runs in close to real time. Results of the method are presented for several examples, including some MRI images with significant amount of noise.
Hidden Markov measure field models for image segmentation
IEEE Transactions on Pattern Analysis and Machine Intelligence, 2003
Parametric image segmentation consists of finding a label field that defines a partition of an image into a set of nonoverlapping regions and the parameters of the models that describe the variation of some property within each region. A new Bayesian formulation for the solution of this problem is presented, based on the key idea of using a doubly stochastic prior model for the label field, which allows one to find exact optimal estimators for both this field and the model parameters by the minimization of a differentiable function. An efficient minimization algorithm and comparisons with existing methods on synthetic images are presented, as well as examples of realistic applications to the segmentation of Magnetic Resonance volumes and to motion segmentation.
On the optimization of probability vector MRFs in image segmentation
2009
Abstract In the context of image segmentation, Markov random fields (MRF) are extensively used. However solution of MRF-based models is heavily dependent on how successfully the MRF energy minimization is performed. In this framework, two methodologies, complementary to each other, are proposed for random field optimization. We address the special class of models comprising a random field imposed on the probabilities of the pixel labels.
Fully Bayesian image segmentation: an engineering perspective
Developments in Markov Chain Monte Carlo procedures have made it possible to perform fully Bayesian image segmentation. By this we mean that all the parameters are treated identically, be they the segmentation labels, the class parameters or the Markov Random Field prior parameters. We perform the analysis by sampling from the posterior distribution of all the parameters. Sampling from the MRF parameters has traditionally been considered if not intractable then at least computationally prohibitive. In the statistics literature there are descriptions of experiments showing that the MRF parameters may be sampled by approximating the partition function. These experiments are all, however, on`toy' problems for the typical size of image encountered in engineering applications phase transition behaviour of the models becomes a major limiting factor in the estimation of the partition function. Nevertheless, we show that with some care, fully Bayesian segmentation can be performed on realistic sized images. We also compare the fully Bayesian approach with the approximate pseudolikelihood method.
2003
Image segmentation methods based on Markovian assumption consist in optimizing a Gibbs energy function which depends on the observation field and the segmented field. This energy function can be represented as a sum of potentials defined on cliques which are subsets of the grid of sites. The Potts model is the most commonly used to represent the segmented field. However, this model only expresses a potential on classes for nearest neighbor pixels. In this paper, we propose the integration of global informations, like the size of a region, in the local potentials of the Gibbs energy. To extract these informations, we use a representation model well known in geometric modeling: the topological map. Results on synthetic and natural images are provided, showing improvements in the obtained segmented fields. § © ¢ ¢ ¢ ¡ §
DECOMPOSITION OF RANGE IMAGES USING MARKOV RANDOM FIELDS
This paper describes a computational model for deriving a decomposition of objects from laser rangefinder data. The process aims to produce a set of parts defined by compactness and smoothness of surface connectivity. Relying on a general decomposition rule, any kind of objects made up of free-form surfaces are partitioned. A robust method to partition the object based on Markov Random Fields (MRF), which allows to incorporate prior knowledge, is presented. Shape index and curvedness descriptors along with discontinuity and concavity distributions are introduced to classify region labels correctly. In addition, a novel way to classify the shape of a surface is proposed resulting in a better distinction of concave, convex and saddle shapes. To achieve a reliable classification a multi-scale method provides a stable estimation of the shape index.