Geodesic Active Contour Model Research Articles

Image segmentation based on adaptive mixture model

As an important research field, image segmentation has attracted considerable attention. The classical geodesic active contour (GAC) model tends to produce fake edges in smooth regions, while the Chan–Vese (CV) model cannot effectively detect images with holes and obtain the precise boundary. To address the above issues, this paper proposes an adaptive mixture model synthesizing the GAC model and the CV model by a weight function. According to image characteristics, the proposed model can adaptively adjust the weight function. In this way, the model exploits the advantages of the GAC model in regions with rich textures or edges, while exploiting the advantages of the CV model in smooth local regions. Moreover, the proposed model is extended to vector-valued images. Through experiments, it is verified that the proposed model obtains better results than the traditional models.

Multiple piecewise constant with geodesic active contours (MPC-GAC) framework for interactive image segmentation using graph cut optimization

This paper proposes an improved variational model, multiple piecewise constant with geodesic active contour (MPC-GAC) model, which generalizes the region-based active contour model by Chan and Vese, 2001 [11] and merges the edge-based active contour by Caselles et al., 1997 [7] to inherit the advantages of region-based and edge-based image segmentation models. We show that the new MPC-GAC energy functional can be iteratively minimized by graph cut algorithms with high computational efficiency compared with the level set framework. This iterative algorithm alternates between the piecewise constant functional learning and the foreground and background updating so that the energy value gradually decreases to the minimum of the energy functional. The k-means method is used to compute the piecewise constant values of the foreground and background of image. We use a graph cut method to detect and update the foreground and background. Numerical experiments show that the proposed interactive segmentation method based on the MPC-GAC model by graph cut optimization can effectively segment images with inhomogeneous objects and background.

An Integrated Region-, Boundary-, Shape-Based Active Contour for Multiple Object Overlap Resolution in Histological Imagery

Active contours and active shape models (ASM) have been widely employed in image segmentation. A major limitation of active contours, however, is in their 1) inability to resolve boundaries of intersecting objects and to 2) handle occlusion. Multiple overlapping objects are typically segmented out as a single object. On the other hand, ASMs are limited by point correspondence issues since object landmarks need to be identified across multiple objects for initial object alignment. ASMs are also are constrained in that they can usually only segment a single object in an image. In this paper, we present a novel synergistic boundary and region-based active contour model that incorporates shape priors in a level set formulation with automated initialization based on watershed. We demonstrate an application of these synergistic active contour models using multiple level sets to segment nuclear and glandular structures on digitized histopathology images of breast and prostate biopsy specimens. Unlike previous related approaches, our model is able to resolve object overlap and separate occluded boundaries of multiple objects simultaneously. The energy functional of the active contour is comprised of three terms. The first term is the prior shape term, modeled on the object of interest, thereby constraining the deformation achievable by the active contour. The second term, a boundary-based term detects object boundaries from image gradients. The third term drives the shape prior and the contour towards the object boundary based on region statistics. The results of qualitative and quantitative evaluation on 100 prostate and 14 breast cancer histology images for the task of detecting and segmenting nuclei and lymphocytes reveals that the model easily outperforms two state of the art segmentation schemes (geodesic active contour and Rousson shape-based model) and on average is able to resolve up to 91% of overlapping/occluded structures in the images.

Active Geodesics: Region-based Active Contour Segmentation with a Global Edge-based Constraint.

We present an active geodesic contour model in which we constrain the evolving active contour to be a geodesic with respect to a weighted edge-based energy through its entire evolution rather than just at its final state (as in the traditional geodesic active contour models). Since the contour is always a geodesic throughout the evolution, we automatically get local optimality with respect to an edge fitting criterion. This enables us to construct a purely region-based energy minimization model without having to devise arbitrary weights in the combination of our energy function to balance edge-based terms with the region-based terms. We show that this novel approach of combining edge information as the geodesic constraint in optimizing a purely region-based energy yields a new class of active contours which exhibit both local and global behaviors that are naturally responsive to intuitive types of user interaction. We also show the relationship of this new class of globally constrained active contours with traditional minimal path methods, which seek global minimizers of purely edge-based energies without incorporating region-based criteria. Finally, we present some numerical examples to illustrate the benefits of this approach over traditional active contour models.

A new method for moving object detection using variable resolution bionic compound eyes

The compound eyes of insect are highly optimized for the task of visual acquisition of relevant information from the environment, such as moving object detection. These have attracted the attention of many researchers in recent years. The advantages of compound eyes are illustrated in this paper in relation to other approaches in moving object detection. The paper describes the imaging mechanism for the compound eyes, and we also describe the process of multi-resolution imaging. An image filter with variable resolution is discussed and we propose a new method for moving object detection using variable resolution double-level contours. Firstly, there is the contour detection which occurs in the lowest resolution images. When this is complete, texture gradient computation is performed which carries out contour segmentation in the high resolution image acquired by the single eye. Finally, a Geodesic Active Contour model for texture boundary detection is applied from which the moving target is recognized. The results in this paper show that this method has good potential as a solution for moving object detection problems.

Image Segmentation Using Binary Level Set Method Based on Region-Based GAC Model

A new Region-based GAC (geodesic active contour) model was presented, which is the improvement of traditional GAC model. A new region-based signed pressure forces function was presented, which takes the place of the edge stopping function, and can efficiently solve the problem of segmentation of objects with weak edges or without edges. The model is implemented by level set method with a binary level set function to reduce the expensive computational cost of re-initialization of the traditional level set function. The proposed algorithm has been applied to images of different modalities with promising results, which are better than that of traditional GAC model and C-V model.

A high-throughput active contour scheme for segmentation of histopathological imagery

In this paper a minimally interactive high-throughput system which employs a color gradient based active contour model for rapid and accurate segmentation of multiple target objects on very large images is presented. While geodesic active contours (GAC) have become very popular tools for image segmentation, they tend to be sensitive to model initialization. A second limitation of GAC models is that the edge detector function typically involves use of gray scale gradients; color images usually being converted to gray scale, prior to gradient computation. For color images, however, the gray scale gradient image results in broken edges and weak boundaries, since the other channels are not exploited in the gradient computation. To cope with these limitations, we present a new GAC model that is driven by an accurate and rapid object initialization scheme; hierarchical normalized cuts (HNCut). HNCut draws its strength from the integration of two powerful segmentation strategies-mean shift clustering and normalized cuts. HNCut involves first defining a color swatch (typically a few pixels) from the object of interest. A multi-scale, mean shift coupled normalized cuts algorithm then rapidly yields an initial accurate detection of all objects in the scene corresponding to the colors in the swatch. This detection result provides the initial contour for a GAC model. The edge-detector function of the GAC model employs a local structure tensor based color gradient, obtained by calculating the local min/max variations contributed from each color channel. We show that the color gradient based edge-detector function results in more prominent boundaries compared to the classical gray scale gradient based function. By integrating the HNCut initialization scheme with color gradient based GAC (CGAC), HNCut-CGAC embodies five unique and novel attributes: (1) efficiency in segmenting multiple target structures; (2) the ability to segment multiple objects from very large images; (3) minimal human interaction; (4) accuracy; and (5) reproducibility. A quantitative and qualitative comparison of the HNCut-CGAC model against other state of the art active contour schemes (including a Hybrid Active Contour model (Paragios-Deriche) and a region-based AC model (Rousson-Deriche)), across 196 digitized prostate histopathology images, suggests that HNCut-CGAC is able to outperform state of the art hybrid and region based AC techniques. Our results show that HNCut-CGAC is computationally efficient and may be easily applied to a variety of different problems and applications.

Multiple piecewise constant with geodesic active contours (MPC-GAC) framework for interactive image segmentation using graph cut optimization

This paper proposes an improved variational model, multiple piecewise constant with geodesic active contour (MPC-GAC) model, which generalizes the region-based active contour model by Chan and Vese, 2001 [11] and merges the edge-based active contour by Caselles et al., 1997 [7] to inherit the advantages of region-based and edge-based image segmentation models. We show that the new MPC-GAC energy functional can be iteratively minimized by graph cut algorithms with high computational efficiency compared with the level set framework. This iterative algorithm alternates between the piecewise constant functional learning and the foreground and background updating so that the energy value gradually decreases to the minimum of the energy functional. The k-means method is used to compute the piecewise constant values of the foreground and background of image. We use a graph cut method to detect and update the foreground and background. Numerical experiments show that the proposed interactive segmentation method based on the MPC-GAC model by graph cut optimization can effectively segment images with inhomogeneous objects and background.

Detecting Water Bodies on RADARSAT Imagery

This paper presents a novel geodesic active contour (GAC) model based on an edge detector for rapid detection of water bodies from spaceborne synthetic aperture radar (SAR) imagery with high speckle noise. The original edge indicator function based on gradients is replaced by an edge indicator function based on the ratio of exponentially weighted averages (ROEWA) operator. Thus, the capability of edge detection and the accuracy of locating edges are greatly improved, which makes the model more appropriate for SAR images. In addition, an enhancing term is added to the original model's energy function in order to boost the strength for the contour's evolution. An unconditionally stable additive operator splitting (AOS) scheme and a fast algorithm for re-initialization of the level set function are adopted, which not only enhances the model's stability, but also speeds up the model's convergence remarkably. The experimental results on simulated and real RADARSAT-1/-2 images show its efficiency and accuracy.

Morphological change tracking of dendritic spines based on structural features

Identification and tracking of dendritic spine morphology from two-dimensional time-lapsed images plays an important role in neurobiological research. Such analysis can enable us to derive a correlation between morphological characteristics and molecular mechanism of dendritic spine development and remodelling. Moreover, Neuronal morphology of hippocampal Cornu Ammonis 1 region is critical for understanding the Alzheimer's disease. Therefore, we need to extract and trace the dendritic spines accurately for examining their development and remodelling processes, which are related to functions of hippocampal Cornu Ammonis 1. There are some problems to be solved in related researches. Noise due to the properties of optical microscopes makes it difficult to identify and trace dendritic spines accurately. To solve these problems, in this paper we present a local spine detection technique minimizing noise influence in two-dimensional optical microscopy images. Also, we suggest an efficient mapping method for tracking the dynamics of dendritic spines to measure their morphological changes quantitatively. First, to utilize structural feature of spines, which are small protrusions of tree-like dendrites, we extract the tips of each dendritic branch and use this position as an initial contour position for a deformable model-based segmentation. We then use a geodesic active contour model to detect the spines accurately. Secondly, we apply an optical flow method, which takes into account both structure and movement of objects, to map every time-series image frame. Proposed method provides accurate measurements of dendritic spine length, volume, shape classification for time-lapse images of dendrites of hippocampal neurons. We compared the proposed spine detection algorithm with manual method performed by biologists and noncommercial software NeuronIQ. In particular, this method is able to segment dendritic spines better than existing methods with high sensitivity in adjacent spines and noisy images. Also the algorithm performs well compared to a human analyser.

Geodesic Active Fields—A Geometric Framework for Image Registration

In this paper we present a novel geometric framework called geodesic active fields for general image registration. In image registration, one looks for the underlying deformation field that best maps one image onto another. This is a classic ill-posed inverse problem, which is usually solved by adding a regularization term. Here, we propose a multiplicative coupling between the registration term and the regularization term, which turns out to be equivalent to embed the deformation field in a weighted minimal surface problem. Then, the deformation field is driven by a minimization flow toward a harmonic map corresponding to the solution of the registration problem. This proposed approach for registration shares close similarities with the well-known geodesic active contours model in image segmentation, where the segmentation term (the edge detector function) is coupled with the regularization term (the length functional) via multiplication as well. As a matter of fact, our proposed geometric model is actually the exact mathematical generalization to vector fields of the weighted length problem for curves and surfaces introduced by Caselles-Kimmel-Sapiro. The energy of the deformation field is measured with the Polyakov energy weighted by a suitable image distance, borrowed from standard registration models. We investigate three different weighting functions, the squared error and the approximated absolute error for monomodal images, and the local joint entropy for multimodal images. As compared to specialized state-of-the-art methods tailored for specific applications, our geometric framework involves important contributions. Firstly, our general formulation for registration works on any parametrizable, smooth and differentiable surface, including nonflat and multiscale images. In the latter case, multiscale images are registered at all scales simultaneously, and the relations between space and scale are intrinsically being accounted for. Second, this method is, to the best of our knowledge, the first reparametrization invariant registration method introduced in the literature. Thirdly, the multiplicative coupling between the registration term, i.e. local image discrepancy, and the regularization term naturally results in a data-dependent tuning of the regularization strength. Finally, by choosing the metric on the deformation field one can freely interpolate between classic Gaussian and more interesting anisotropic, TV-like regularization.

Boundary Detection in Medical Images Using Edge Following Algorithm Based on Intensity Gradient and Texture Gradient Features

Finding the correct boundary in noisy images is still a difficult task. This paper introduces a new edge following technique for boundary detection in noisy images. Utilization of the proposed technique is exhibited via its application to various types of medical images. Our proposed technique can detect the boundaries of objects in noisy images using the information from the intensity gradient via the vector image model and the texture gradient via the edge map. The performance and robustness of the technique have been tested to segment objects in synthetic noisy images and medical images including prostates in ultrasound images, left ventricles in cardiac magnetic resonance (MR) images, aortas in cardiovascular MR images, and knee joints in computerized tomography images. We compare the proposed segmentation technique with the active contour models (ACM), geodesic active contour models, active contours without edges, gradient vector flow snake models, and ACMs based on vector field convolution, by using the skilled doctors' opinions as the ground truths. The results show that our technique performs very well and yields better performance than the classical contour models. The proposed method is robust and applicable on various kinds of noisy images without prior knowledge of noise properties.

Robust contour tracking based on a coupling between geodesic active contours and conditional random fields

This paper presents a new general framework for contour tracking based on the synergy of two powerful segmentation tools, namely, spatial temporal conditional random fields (CRFs) and geodesic active contours (GACs). The contours of targets are modeled using a level set representation. The evolution of the level sets toward the target contours is formulated as one of the joint region-based (CRF) and boundary-based (GAC) segmentations under a unified Bayesian framework. A variational inference technique is used to solve this otherwise intractable inference problem, leading to approximate MAP solutions of both the new 3D spatial temporal CRF and the GAC model. The tracking result of the previous frame is used to initialize the curve in the current frame. Typical contour tracking problems are considered and experimental results are given to illustrate the robustness of the method against noise and its accurate performance in moving objects boundary localization.

Three-dimensional organ modeling based on deformable surfaces applied to radio-oncology

This paper describes a method based on an energy minimizing deformable model applied to the 3D biomechanical modeling of a set of organs considered as regions of interest (ROI) for radiotherapy. The initial model consists of a quadratic surface that is deformed to the exact contour of the ROI by means of the physical properties of a mass-spring system. The exact contour of each ROI is first obtained using a geodesic active contour model. The ROI is then parameterized by the vibration modes resulting from the deformation process. Once each structure has been defined, the method provides a 3D global model including the whole set of ROIs. This model allows one to describe statistically the most significant variations among its structures. Statistical ROI variations among a set of patients or through time can be analyzed. Experimental results are presented using the pelvic zone to simulate anatomical variations among structures and its application in radiotherapy treatment planning.

Expectation–Maximization-Driven Geodesic Active Contour With Overlap Resolution (EMaGACOR): Application to Lymphocyte Segmentation on Breast Cancer Histopathology

The presence of lymphocytic infiltration (LI) has been correlated with nodal metastasis and tumor recurrence in HER2+ breast cancer (BC). The ability to automatically detect and quantify extent of LI on histopathology imagery could potentially result in the development of an image based prognostic tool for human epidermal growth factor receptor-2 (HER2+) BC patients. Lymphocyte segmentation in hematoxylin and eosin (H&E) stained BC histopathology images is complicated by the similarity in appearance between lymphocyte nuclei and other structures (e.g., cancer nuclei) in the image. Additional challenges include biological variability, histological artifacts, and high prevalence of overlapping objects. Although active contours are widely employed in image segmentation, they are limited in their ability to segment overlapping objects and are sensitive to initialization. In this paper, we present a new segmentation scheme, expectation-maximization (EM) driven geodesic active contour with overlap resolution (EMaGACOR), which we apply to automatically detecting and segmenting lymphocytes on HER2+ BC histopathology images. EMaGACOR utilizes the expectation-maximization algorithm for automatically initializing a geodesic active contour (GAC) and includes a novel scheme based on heuristic splitting of contours via identification of high concavity points for resolving overlapping structures. EMaGACOR was evaluated on a total of 100 HER2+ breast biopsy histology images and was found to have a detection sensitivity of over 86% and a positive predictive value of over 64%. By comparison, the EMaGAC model (without overlap resolution) and GAC model yielded corresponding detection sensitivities of 42% and 19%, respectively. Furthermore, EMaGACOR was able to correctly resolve over 90% of overlaps between intersecting lymphocytes. Hausdorff distance (HD) and mean absolute distance (MAD) for EMaGACOR were found to be 2.1 and 0.9 pixels, respectively, and significantly better compared to the corresponding performance of the EMaGAC and GAC models. EMaGACOR is an efficient, robust, reproducible, and accurate segmentation technique that could potentially be applied to other biomedical image analysis problems.

A New Variational Model for Segmenting Objects of Interest from Color Images

We propose a new variational model for segmenting objects of interest from color images. This model is inspired by the geodesic active contour model, the region-scalable fitting model, the weighted bounded variation model and the active contour models based on the Mumford-Shah model. In order to segment desired objects in color images, the energy functional in our model includes a discrimination function that determines whether an image pixel belongs to the desired objects or not. Compared with other active contour models, our new model cannot only avoid the usual drawback in the level set approach but also detect the objects of interest accurately. Moreover, we investigate the new model mathematically and establish the existence of the minimum to the new energy functional. Finally, numerical results show the effectiveness of our proposed model.

视觉注意驱动的测地线主动轮廓模型及其应用

视觉注意驱动的测地线主动轮廓模型及其应用

Image segmentation method using binary level set based on regional GAC model

A new model of Geodesic Active Contour(GAC)based on region was presented,which was the improvement of traditional GAC model.A new region-based signed pressure forces function was constructed,which took the place of the edge stopping function,and could efficiently solve the problem of objects segmentation with weak edges or without edges.The model was implemented by level set method with a binary level set function to reduce the expensive computational cost of re-initialization of the traditional level set function.The proposed algorithm has been applied to images of different modalities,and the results are better than that of traditional GAC model and C-V model.

Anisotropic Cheeger Sets and Applications

The main purpose of this paper is to develop the mathematical analysis of anisotropic total variation problems with a degenerate metric and the computation of the associated Cheeger sets. We illustrate our analysis with the computation of Cheeger sets with respect to different anisotropic norms of relevance in applications to image processing. In particular, we describe the computation of global minima of geodesic active contour models, and we illustrate the use of Cheeger sets for the problem of edge linking.

Precise center location for light spot contour images of light emitting diode control points in light-pen vision coordinate measurement

In a light-pen single-camera three-dimensional (3-D) coordinate vision measurement system, a key step is the fast and precise center location for the light spot contour images of the LED control points obtained by the charge-coupled device (CCD) camera. A novel center location scheme for the light spot contour images is proposed in this key step. This scheme uses a geodesic active contour model to obtain every light spot's contour edge simultaneously. Then the center coordinate of every light spot is measured using a subpixel scheme. Compared to the common scheme using the edge detection and the contour tracking, this scheme is highly precise and fast for the center location of every light spot in a CCD image.