Interactive free-form level-set surface-editing operators

We present a level set framework for implementing editing operators for surfaces. Level set models are deformable implicit surfaces where the deformation of the surface is controlled by a speed function in the level set partial differential equation. In this paper we define a collection of speed functions that produce a set of surface editing operators. The speed functions describe the velocity at each point on the evolving surface in the direction of the surface normal. All of the information needed to deform a surface is encapsulated in the speed function, providing a simple, unified computational framework. The user combines pre-defined building blocks to create the desired speed function. The surface editing operators are quickly computed and may be applied both regionally and globally. The level set framework offers several advantages. 1) By construction, self-intersection cannot occur, which guarantees the generation of physically-realizable, simple, closed surfaces. 2) Level set models easily change topological genus, and 3) are free of the edge connectivity and mesh quality problems associated with mesh models. We present five examples of surface editing operators: blending, smoothing, sharpening, openings/closings and embossing. We demonstrate their effectiveness on several scanned objects and scan-converted models.

We propose an approach to region tracking that is derived from a Bayesian formulation. The novelty of the approach is twofold. First, no motion field or motion parameters need to be computed. This removes a major burden since accurate motion computation has been and remains a challenging problem and the quality of region tracking algorithms based on motion critically depends on the computed motion fields and parameters. The second novelty of this approach, is that very little a priori information about the region being tracked is used in the algorithm. In particular, unlike numerous tracking algorithms, no assumption is made on the strength of the intensity edges of the boundary of the region being tracked, nor is its shape assumed to be of a certain parametric form. The problem of region tracking is formulated as a Bayesian estimation problem and the resulting tracking algorithm is expressed as a level set partial differential equation. We present further extensions to this partial differential equation, allowing the possibility of including additional information in the tracking process, such as priors on the region's intensity boundaries and we present the details of the numerical implementation. Very promising experimental results are provided.

Detail-preserving level set surface editing and geometric texture transfer

Image segmentation plays an important role in computer vision and image processing. Level set model is a classical image segmentation method. During level set evolution, almost all the level set energy minimization of image segmentation are based on the gradient descent method and the finite difference scheme. The speed of evolution is slow and easy to fall into local minima. In this paper, we propose a fast sweeping optimization algorithm to minimize global cosine fitting (GCF) model. When moving a pixel from the one side region to the another side region of evolving contour, the sweeping algorithm calculates the energy change directly and checks whether the cosine fitting energy is decreased. With this, we can avoid solving the Euler-Lagrange equation and the partial differential equation, which usually take a lot of time. Moreover, our proposal is robust to initial level set contour and it automatically handles the topological variety, algorithm automatic termination and no longer requires the reinitialization step, parameter adjustment and the distance regularization term. The experiments on real noise and synthetic images show the effectiveness of the sweeping algorithm.

Concurrent two-scale topological design of multiple unit cells and structure using combined velocity field level set and density model

In this paper we present an innovative and automatic procedure which is used to extract the coastline from SAR (Synthetic Aperture Radar) images by the level set model. This model consists in a PDE (Partial Differential Equation) equation governing the evolution of a curve corresponding to the zero level of a 3D function, called level set function, until the curve reaches the edge of the region to be segmented. A coastline is the boundary between land and sea masses. Detecting the coastline is of fundamental importance when monitoring various natural phenomena such as tides, coastal erosion and the dynamics of glaciers. In this case SAR images show problems which arise from the presence of the speckle noise and of the strong signal deriving from the rough or slight sea. In fact in the case of heavy sea the signal determines an intensity similar to the one of land, making it difficult to distinguish the coastline.KeywordsActive ContourSynthetic Aperture RadarInitial CurveSpeckle NoiseSpeed FunctionThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

In this paper, we propose a novel algorithm for region tracking without motion computation that uses as its starting point the Bayesian framework for tracking previously developed [A.-R. Mansouri, July 2002], [A.R. Mansouri, A. Mitiche, 2002], extending it to a multi-frame tracking algorithm in which tracking is expressed as segmentation in the spatio-temporal domain [A.Mitiche, et al., April 2002]. Our proposed algorithm is expressed as the solution of level set partial differential equations and the tracked region in a particular frame of the sequence is then obtained as the time slice of the level surface given by the level set equations. The main benefit of our proposed algorithm is that contrary to numerous other tracking algorithms, it is a multi-frame tracking algorithm which does not assume the motion to be small [M. Bertalmio, et al., 1998], nor the background to be stationary [S. Jehan-Besson, et al., 2000], nor the region to be uniform in intensity on a uniform background [N. Paragios, R. Deriche, 2000], nor does it assume any motion models [A. Mitiche, et al., April 2002]. This leads to a tracking algorithm which combines the advantages of the Bayesian formulation developed for frame-to-frame tracking [A.-R. Mansouri, July 2002] with those of the formulation in the spatio-temporal domain [A. Mitiche, et al., April 2002]. We illustrate the performance of our algorithm on real image sequences with natural motion.

The purpose of this study is to investigate a method of tracking moving objects with a moving camera. This method interprets tracking as detection of the surface generated by motion boundaries in the spatio-temporal domain and estimates simultaneously the motion induced by camera movement. The problem is formulated as a Bayesian motion-based partitioning problem in the spatio-temporal domain of the image sequence. An energy functional is derived from the Bayesian formulation. The Euler Lagrange descent equations determine simultaneously an estimate of the image motion field induced by camera motion and an estimate of the spatio-temporal motion boundary surface. The Euler-Lagrange equation corresponding to the surface is expressed as a level set partial differential equation for topology independence and numerically stable implementation. The method has a simple initialization and allows the tracking of multiple objects with non simultaneous motions. Optical velocities on motion boundaries is estimated from geometrical properties of the motion boundary surface. Several examples of experimental verification are given using synthetic and real image sequences.

Segmentation of hippocampus in the brain is one of a major challenge in medical image segmentation due to its’ imaging characteristics, with almost similar intensity between another adjacent gray matter structure, such as amygdala. The intensity similarity has causes the hippocampus to have weak or fuzzy boundaries. With this main challenge being demonstrated by hippocampus, a segmentation method that relies on image information alone may not produce accurate segmentation results. Therefore, it is needed an assimilation of prior information such as shape and spatial information into existing segmentation method to produce the expected segmentation. Previous studies has widely integrated prior information into segmentation methods. However, the prior information has been utilized through a global manner integration, and this does not reflect the real scenario during clinical delineation. Therefore, in this paper, a locally integrated prior information into a level set model is presented. This work utilizes a mean shape model to provide automatic initialization for level set evolution, and has been integrated as prior information into the level set model. The local integration of edge based information and prior information has been implemented through an edge weighting map that decides at voxel level which information need to be observed during a level set evolution. The edge weighting map shows which corresponding voxels having sufficient edge information. Experiments shows that the proposed integration of prior information locally into a conventional edge-based level set model, known as geodesic active contour has shown improvement of 9% in averaged Dice coefficient.

Segmentation of the target object(s) from images that have multiple complicated regions, mixture intensity distributions or are corrupted by noise poses a challenge for the level set models. In addition, the conventional piecewise smooth level set models normally require prior knowledge about the number of image segments. To address these problems, we propose a novel segmentation energy function with two distribution descriptors to model the background and the target. The single background descriptor models the heterogeneous background with multiple regions. Then, the target descriptor takes into account the intensity distribution and incorporates local spatial constraint. Our descriptors, which have more complete distribution information, construct the unique energy function to differentiate the target from the background and are more tolerant of image noise. We compare our approach to three other level set models: 1) the Chan-Vese; 2) the multiphase level set; and 3) the geodesic level set. This comparison using 260 synthetic images with varying levels and types of image noise and medical images with more complicated backgrounds showed that our method outperforms these models for accuracy and immunity to noise. On an additional set of 300 synthetic images, our model is also less sensitive to the contour initialization as well as to different types and levels of noise.

The edge-based level set model gives no satisfactory results for images with weak edge, and the region-based model performs poorly for intensity inhomogeneity images. In this paper, we propose an improved region-based level set model that integrates both the gradient information and the region information. The proposed model defines a novel external energy term, which consists of gradient information and signed pressure forces function. In order to eliminate the re-initialization procedure of traditional level set model, an internal energy term is also introduced for the level set function to maintain signed distance function. Compared with traditional models, our model is more robust against images with weak edge and intensity inhomogeneity. Experiments on liver segmentation from abdominal CT images demonstrate the effectiveness and accuracy of the proposed method.

Regional level set method is a popular approach for image segmentation that uses inside and outside information of contour to extract object boundary. Unfortunately, in many cases, such method is not adequate to model complex textured objects. In this paper, we propose a natural texture image segmentation method which incorporates the pixel-level feature into region-level feature. The multiscale local structure operation is proposed as pixel-level feature to describe the texture structure of image. So the problems of multi-scale and rotation invariance of inhomogeneous texture are addressed by introducing multi-scale local structure operation into level set energy functional. Then, the global intensity information is extracted as the region-level feature and integrated with multi-scale local structure operation. Further, we propose a so-called vector level set method to obtain the segmentation results. Here, we extend the traditional regional level set model into the vector formulation so that the multi-scale local structure operation can be suitably combined with the global intensity information to achieve the more superior image segmentation performance than that of the traditional segmentation methods for texture images. Experiments on some synthesis texture images and real natural scene images demonstrate the excellent performance of the proposed method which successfully combines local structure information and global intensity information to extract the object boundary.

This paper proposes a new method for melasma pigmentary area segmentation utilizing re action-diffusion based level set model (RDLSM) together with local entropy thresholding. In the adopted level set model, a diffusion term is used to regularize the level set function while a reaction term with anticipated sign property is used to force the zero level set towards desired locations. Then local entropy thresholding is applied to address the over-segmentation issue of RDLSM and to extract desired boundaries with higher overall local entropy. As a result, the melasma pigmentary areas and the normal skin areas can be better identified. Experimental results show that the proposed method performs well for melasma image segmentation, especially for cases with severe non-uniform illumination distribution.

Active contour model (ACM) approaches for image segmentation and feature extraction have emerged as very appealing and powerful tools in image processing. The basis of ACM approach is to evolve a curve, called level set, to extract the desired object (s) under some constraints. In this course, various extensions of earlier Osher's level set model have been suggested in the litareture. More recently, a new ACM model referred to selective binary and Gaussian filtering regularized level set (SBGFRIL) has been put forward as a fruitful combination of geodesic active contour model (GAC) and Chan-Vese (C-V) active contour models. This paper attempts to put forward some appealing performance indices to assess the performances of the suggested SBGFRIL compared with GAC and V-C models. The performance metrics involve the clustering based quality evaluations.

We present a supervised Classification model based on a variational approach. This model is devoted to find an optimal partition compound of homogeneous classes with regular interfaces. We represent the regions of the image defined by the classes and their interfaces by level set functions, and we define a functional whose minimum is an optimal partition. The coupled Partial Differential Equations (PDE) related to the minimization of the functional are considered through a dynamical scheme. Given an initial interface set (zero level set), the Different terms of the PDE's are governing the motion of interfaces such that, at convergence, we get an optimal partition as defined above. Each interface is guided by internal forces (regularity of the interface), and external ones (data term, no vacuum, no regions overlapping). Several experiments were conducted on both synthetic an real images.