A Summary of Geometric Level-Set Analogues for a General Class of Parametric Active Contour and Surface Models

© 2001 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.DOI: 10.1109/VLSM.2001.938888Geometric active contours (GACs) and surfaces (GASs) implemented via level set techniques enjoy many advantages over parametric active contours (PACs) and surfaces (PASs), such as computational stability and the ability to change topology during deformation. While many capabilities of earlier PACs and PASs have been reproduced by various GACs and GASs, and while relationships have been discussed for a variety of specific cases, a comprehensive accounting of the connections between these two worlds (particularly regarding rigid forces) has not been consolidated thus far. In this paper we present the precise mathematical relationships between the two for an extensive family of both active contour and surface models, encompassing spatially-varying coefficients, both tension and rigidity, and both conservative and non-conservative external forces. The result is a very general geometric formulation for which the intuitive design principles of PACs and PASs can be applied. We also point out which type of PAC and PAS methodologies cannot be adapted to the geometric level set framework. We conclude by demonstrating several geometric adaptations of specfic PACs and PASs in several simulations

Levelset and B-spline deformable model techniques for image segmentation: a pragmatic comparative study

International audienceDeformable contours are now widely used in image segmentation, using different models, criteria and numerical schemes. Some theoretical comparisons between some deformable model methods have already been published. Yet, very few experimental comparative studies on real data have been reported. In this paper,we compare a levelset with a B-spline based deformable model approach in order to understand the mechanisms involved in these widely used methods and to compare both evolution and results on various kinds of image segmentation problems. In general, both methods yield similar results. However, specific differences appear when considering particular problems

Fully Deformable 3D Digital Partition Model with Topological Control

International audienceWe propose a purely discrete deformable partition model for segmenting 3D images. Its main ability is to maintain the topology of the partition during the minimization process. To do so, our main contribution is a new definition of multi-label simple points (ML simple point) that is easily computable. An ML simple point can be relabeled without modifying the overall topology of the partition. The definition is based on intervoxel properties, and uses the notion of collapse on cubical complexes. This work is an extension of a former restricted definition [DupasAl09] that prohibits the move of intersections of boundary surfaces. A deformation process is carried out with a greedy energy minimization algorithm. A discrete area estimator is used to approach at best standard regularizers classically used in continuous energy minimizing methods. We illustrate the potential of our approach with the segmentation of 3D medical images with known expected topology

Variational methods for texture segmentation

In the last decades, image production has grown significantly. From digital photographs to the medical scans, including satellite images and video films, more and more data need to be processed. Consequently the number of applications based on digital images has increased, either for medicine, research for country planning or for entertainment business such as animation or video games. All these areas, although very different one to another, need the same image processing techniques. Among all these techniques, segmentation is probably one of the most studied because of its important role. Segmentation is the process of extracting meaningful objects from an image. This task, although easily achieved by the human visual system, is actually complex and still a true challenge for the image processing community despite several decades of research. The thesis work presented in this manuscript proposes solutions to the image segmentation problem in a well established mathematical framework, i.e. variational models. The image is defined in a continuous space and the segmentation problem is expressed through a functional or energy optimization. Depending on the object to be segmented, this energy definition can be difficult; in particular for objects with ambiguous borders or objects with textures. For the latter, the difficulty lies already in the definition of the term texture. The human eye can easily recognize a texture, but it is quite difficult to find words to define it, even more in mathematical terms. There is a deliberate vagueness in the definition of texture which explains the difficulty to conceptualize a model able to describe it. Often these textures can neither be described by homogeneous regions nor by sharp contours. This is why we are first interested in the extraction of texture features, that is to say, finding one representation that can discriminate a textured region from another. The first contribution of this thesis is the construction of a texture descriptor from the representation of the image similar to a surface in a volume. This descriptor belongs to the framework of non-supervised segmentation, since it will not require any user interaction. The second contribution is a solution for the segmentation problem based on active contour models and information theory tools. Third contribution is a semi-supervised segmentation model, i.e. where constraints provided by the user will be integrated in the segmentation framework. This processus is actually derived from the graph of image patches. This graph gives the connectivity measure between the different points of the image. The segmentation will be expressed by a graph partition and a variational model. This manuscript proposes to tackle the segmentation problem for textured images

Information Extraction and Modeling from Remote Sensing Images: Application to the Enhancement of Digital Elevation Models

To deal with high complexity data such as remote sensing images presenting metric resolution over large areas, an innovative, fast and robust image processing system is presented. The modeling of increasing level of information is used to extract, represent and link image features to semantic content. The potential of the proposed techniques is demonstrated with an application to enhance and regularize digital elevation models based on information collected from RS images

Model extensions and applications in mathematical imaging.

Mathematical imaging consists of many different applications including image segmentation, image classification, and inpainting. This work deals more specifically with image segmentation: the partition of an image into the background and the objects present in the image. The main focus is the active contours without gradient model by Tony Chan and Luminita Vese which deals with fitting a curve imbedded in the plane image. The fitting of the curve comes from an evolutionary partial differential equation. The dissertation contributes three novel ideas: a linearized version of the active contours without gradient model published in [20]; a new procedure using fourth order fitting terms in place of the second order fitting terms which gives faster segmentation and may be used to provide a good initial condition; a novel way of tracking regions present in bulk data in order to gain an understanding of macroscopic details associated with some physical application. Results include images showing the accuracy of the segmentation for the methods, a discussion of the choice of initial condition, and discussion of feasibility for the data tracking. These results compare to those obtained with the nonlinear model and serve as a proof-of-concept for further investigation. The dissertation ends with a discussion of future research

A collaborative approach to image segmentation and behavior recognition from image sequences

Visual behavior recognition is currently a highly active research area. This is due both to the scientific challenge posed by the complexity of the task, and to the growing interest in its applications, such as automated visual surveillance, human-computer interaction, medical diagnosis or video indexing/retrieval. A large number of different approaches have been developed, whose complexity and underlying models depend on the goals of the particular application which is targeted. The general trend followed by these approaches is the separation of the behavior recognition task into two sequential processes. The first one is a feature extraction process, where features which are considered relevant for the recognition task are extracted from the input image sequence. The second one is the actual recognition process, where the extracted features are classified in terms of the pre-defined behavior classes. One problematic issue of such a two-pass procedure is that the recognition process is highly dependent on the feature extraction process, and does not have the possibility to influence it. Consequently, a failure of the feature extraction process may impair correct recognition. The focus of our thesis is on the recognition of single object behavior from monocular image sequences. We propose a general framework where feature extraction and behavior recognition are performed jointly, thereby allowing the two tasks to mutually improve their results through collaboration and sharing of existing knowledge. The intended collaboration is achieved by introducing a probabilistic temporal model based on a Hidden Markov Model (HMM). In our formulation, behavior is decomposed into a sequence of simple actions and each action is associated with a different probability of observing a particular set of object attributes within the image at a given time. Moreover, our model includes a probabilistic formulation of attribute (feature) extraction in terms of image segmentation. Contrary to existing approaches, segmentation is achieved by taking into account the relative probabilities of each action, which are provided by the underlying HMM. In this context, we solve the joint problem of attribute extraction and behavior recognition by developing a variation of the Viterbi decoding algorithm, adapted to our model. Within the algorithm derivation, we translate the probabilistic attribute extraction formulation into a variational segmentation model. The proposed model is defined as a combination of typical image- and contour-dependent energy terms with a term which encapsulates prior information, offered by the collaborating recognition process. This prior information is introduced by means of a competition between multiple prior terms, corresponding to the different action classes which may have generated the current image. As a result of our algorithm, the recognized behavior is represented as a succession of action classes corresponding to the images in the given sequence. Furthermore, we develop an extension of our general framework, that allows us to deal with a common situation encountered in applications. Namely, we treat the case where behavior is specified in terms of a discrete set of behavior types, made up of different successions of actions, which belong to a shared set of action classes. Therefore, the recognition of behavior requires the estimation of the most probable behavior type and of the corresponding most probable succession of action classes which explains the observed image sequence. To this end, we modify our initial model and develop a corresponding Viterbi decoding algorithm. Both our initial framework and its extension are defined in general terms, involving several free parameters which can be chosen so as to obtain suitable implementations for the targeted applications. In this thesis, we demonstrate the viability of the proposed framework by developing particular implementations for two applications. Both applications belong to the field of gesture recognition and concern finger-counting and finger-spelling. For the finger-counting application, we use our original framework, whereas for the finger-spelling application, we use its proposed extension. For both applications, we instantiate the free parameters of the respective frameworks with particular models and quantities. Then, we explain the training of the obtained models from specific training data. Finally, we present the results obtained by testing our trained models on new image sequences. The test results show the robustness of our models in difficult cases, including noisy images, occlusions of the gesturing hand and cluttered background. For the finger-spelling application, a comparison with the traditional sequential approach to image segmentation and behavior recognition illustrates the superiority of our collaborative model

High performance computing for 3D image segmentation

Digital image processing is a very popular and still very promising eld of science, which has been successfully applied to numerous areas and problems, reaching elds like forensic analysis, security systems, multimedia processing, aerospace, automotive, and many more. A very important part of the image processing area is image segmentation. This refers to the task of partitioning a given image into multiple regions and is typically used to locate and mark objects and boundaries in input scenes. After segmentation the image represents a set of data far more suitable for further algorithmic processing and decision making. Image segmentation algorithms are a very broad eld and they have received signi cant amount of research interest A good example of an area, in which image processing plays a constantly growing role, is the eld of medical solutions. The expectations and demands that are presented in this branch of science are very high and dif cult to meet for the applied technology. The problems are challenging and the potential bene ts are signi cant and clearly visible. For over thirty years image processing has been applied to different problems and questions in medicine and the practitioners have exploited the rich possibilities that it offered. As a result, the eld of medicine has seen signi cant improvements in the interpretation of examined medical data. Clearly, the medical knowledge has also evolved signi cantly over these years, as well as the medical equipment that serves doctors and researchers. Also the common computer hardware, which is present at homes, of ces and laboratories, is constantly evolving and changing. All of these factors have sculptured the shape of modern image processing techniques and established in which ways it is currently used and developed. Modern medical image processing is centered around 3D images with high spatial and temporal resolution, which can bring a tremendous amount of data for medical practitioners. Processing of such large sets of data is not an easy task, requiring high computational power. Furthermore, in present times the computational power is not as easily available as in recent years, as the growth of possibilities of a single processing unit is very limited - a trend towards multi-unit processing and parallelization of the workload is clearly visible. Therefore, in order to continue the development of more complex and more advanced image processing techniques, a new direction is necessary. A very interesting family of image segmentation algorithms, which has been gaining a lot of focus in the last three decades, is called Deformable Models. They are based on the concept of placing a geometrical object in the scene of interest and deforming it until it assumes the shape of objects of interest. This process is usually guided by several forces, which originate in mathematical functions, features of the input images and other constraints of the deformation process, like object curvature or continuity. A range of very desired features of Deformable Models include their high capability for customization and specialization for different tasks and also extensibility with various approaches for prior knowledge incorporation. This set of characteristics makes Deformable Models a very ef cient approach, which is capable of delivering results in competitive times and with very good quality of segmentation, robust to noisy and incomplete data. However, despite the large amount of work carried out in this area, Deformable Models still suffer from a number of drawbacks. Those that have been gaining the most focus are e.g. sensitivity to the initial position and shape of the model, sensitivity to noise in the input images and to awed input data, or the need for user supervision over the process. The work described in this thesis aims at addressing the problems of modern image segmentation, which has raised from the combination of above-mentioned factors: the signi cant growth of image volumes sizes, the growth of complexity of image processing algorithms, coupled with the change in processor development and turn towards multi-processing units instead of growing bus speeds and the number of operations per second of a single processing unit. We present our innovative model for 3D image segmentation, called the The Whole Mesh Deformation model, which holds a set of very desired features that successfully address the above-mentioned requirements. Our model has been designed speci cally for execution on parallel architectures and with the purpose of working well with very large 3D images that are created by modern medical acquisition devices. Our solution is based on Deformable Models and is characterized by a very effective and precise segmentation capability. The proposed Whole Mesh Deformation (WMD) model uses a 3D mesh instead of a contour or a surface to represent the segmented shapes of interest, which allows exploiting more information in the image and obtaining results in shorter times. The model offers a very good ability for topology changes and allows effective parallelization of work ow, which makes it a very good choice for large data-sets. In this thesis we present a precise model description, followed by experiments on arti cial images and real medical data