Edge Indicator Function Research Articles

Level Sets Guided by SoDEF-Fitting Energy for River Channel Detection in SAR Images

To achieve river channel detection in SAR (synthetic aperture radar) images, we developed a level-set-based model (LSBM) guided by a designed data-fitting energy which is called the SoDEF (sum of dual exponential functions)-fitting energy. Firstly, we designed a function by computing the sum of dual exponential functions to substitute for the quadratic function, and used it to construct the data-fitting energy. Secondly, the adaptive area-fitting centers (AFCs) were computed based on two kinds of grayscale characteristics, which are more accurate and more stable. Thirdly, the Dirac function in gradient descent flow was displaced by an edge indicator function to help the evolving level sets stop at the target edges. Moreover, some regularized terms were incorporated into the objective function to guarantee the model’s stability. The river channel detection experiments conducted with real SAR images indicated that the developed model is superior to the related state-of-the-art methods in its detection accuracy and efficiency.

Dynamic iris inner edge location method based on distance-regularized level set

Iris localization is an important part of iris recognition. Aiming at the influence of irregular pupil circle and illumination inequality in dynamic iris localization in actual scene, a dynamic iris inner edge location method based on distance regularized level set model was proposed. According to the geometric features of iris, the pupil and iris are coarsely located through the secondary projection of binary image, and the initial contour of evolution of horizontal set is determined. Accurate positioning of the inner edge of iris is achieved by the improved distance regularized level set model of edge indicator function. Iris images Database were respectively experimented with this paper and another improved distance regularized level set model, and the positioning effect was evaluated by using the Jakard similarity coefficient. The results show that the distance regularized level set model based dynamic iris internal edge localization algorithm proposed in this paper can significantly reduce the number of iterations and positioning time of the localization algorithm on the basis of ensuring the positioning accuracy,which provides a theoretical basis and technical reference for the application of iris recognition technology.

Accurate image segmentation based on adaptive distance regularization level set method

Level set method has been widely applied in the field of image segmentation. However, the level set formulation is inevitably affected by the regularization function, in-homogeneity and weak edge in the process of evolution, which often leads to the instability and inaccuracy of image segmentation results. To solve these problems, a new distance regularization term defined by a double-well potential function is proposed to satisfy more ideal characteristics of signed distance property. In addition, a novel edge indicator function is introduced to segment images with uneven intensity or weak edge. Finally, the adaptive adjustment formulas of distance regularization and area parameters are derived to alleviate the difficulty of parameter adjustment. Experimental results show that the proposed model provides better accuracy and versatility, quantitative experiment on Weizmann segmentation evaluation database achieves mean Dice score (96.87%), IoU (94.38%), Hausdorff distance (3.20[Formula: see text]mm), Recall (97.68%) and Precision (96.32%), respectively.

A hybrid active contour model based on pre-fitting energy and adaptive functions for fast image segmentation

• An adaptive edge indicator function is proposed to make evolution process more stable and robust to initial contours. • An adaptive sign function is proposed to enable the evolution curve to adjust evolution direction and speed. • New pre-fitting functions are computed before the iteration without online update to reduce computation cost. • A single-well potential function is provided to prevent segmentation failure and increase segmentation speed. In this study, a hybrid active contour model driven by pre-fitting energy with an adaptive edge indicator function and an adaptive sign function is proposed. The key idea of employing the pre-fitting energy is to define two pre-fitting functions to calculate mean intensities of two sub-regions separated from the selected local region based on pre-calculated median intensity of the selected local region before the curve evolves, which saves a huge amount of computation cost. In addition, a brand-new single-well potential function and its associated evolution speed function are put forward to enable evolution process to converge faster as well as more robust. Experimental outcomes indicate that this model is competent to obtain motion boundaries of different targets effectively and efficiently. Compared with traditional models and recently developed models, this model not only reduces the CPU running time and iteration number significantly as well as improves segmentation accuracies (Dice similarity coefficient (DSC) and Jaccard similarity coefficient (JSC)), but also exhibits insensitivity to initialization.

Hybrid active contour model driven by optimized local pre-fitting image energy for fast image segmentation

In this paper, the hybrid active contour model driven by optimized local pre-fitting image (OLPFI) energy was proposed for fast image segmentation. Since the proposed model combines the local pre-fitted image (LPFI) function with region-based characteristic and the optimized edge indicator function with edge-based characteristic, the proposed model can not only correctly segment images with intensity inhomogeneity or weak boundaries, but also can deal with images whose target has large noise interference inside. The two pre-fitting functions are computed before curve evolution, so the computational cost of the proposed model reduces greatly. Furthermore, the evolution curve can adaptively select the motion direction according to image information because of energy sign function. Regularized function used in the proposed model can accelerate the segmentation speed of the proposed model. Moreover, the addition of the regularization term and length term helps to improve segmentation efficiency of the proposed model and eliminate the effect of sensitive parameters in traditional penalty and length terms. Experimental results show that the proposed model has great efficiency in segmenting images and great robustness on initialization and parameters.

A robust hybrid active contour model based on pre-fitting bias field correction for fast image segmentation

An array of existing active contour models is prone to suffering from the deficiencies of poor anti-noise ability, initialization sensitivity, and slow convergence. In order to handle these problems, a robust hybrid active contour method based on bias correction is proposed in this research paper The energy functional is formulated through incorporating the adaptive edge indicator function and level set formulation driven by bias field correction. The adaptive edge indicator function, which is formulated based on image gradient information, is utilized to detect object boundaries and accelerate the segmentation in the homogeneous region. The level set formulation is constructed based on an improved criterion function, in which bias field information is considered. Specifically, the bias field distribution is approximated through the local mean gray value algorithm as a prior. Moreover, a new regularized function is proposed so as to maintain the stability of curve evolution. The segmentation process is implemented by the optimized energy function and the novel regularized term. Compared to previous active contour models, the modified active contour method can yield more precise, stable, and efficient segmentation results on some challenging images.

Cartoon and Texture Image Decomposition Driven by Weighted Curvature

In this paper, we propose a curvature-guided model with divergence-free constraints to facilitate image decomposition. Since basic TV regularization has difficulty in processing edge geometry information of cartoon image, in order to preserve the edge features, we introduce a level set curvature term to smooth the uniform area, and use the edge indicator function as the weighted regularization to preserve the edge. In addition, to control the smoothness, a gradient function is proposed to balance the edge indicator function and the curvature term. On the other hand, we find that the existing partial decomposition models measure the oscillation function with the $H^{-1}$ functional, but this functional ignores the divergence-free vector field during the Hodge decomposition process, then the texture will lose some vector direction information, and then affects the decomposition results. By analyzing the theory of divergence-free vector field, a new decomposition model with the constraint of divergence-free vector field is proposed in this paper. Numerical experiments show that the proposed model can well preserves the edges of cartoon and protects the texture of repetitive patterns.

Edge-guided second-order total generalized variation for Gaussian noise removal from depth map

Total generalized variation models have recently demonstrated high-quality denoising capacity for single image. In this paper, we present an accurate denoising method for depth map. Our method uses a weighted second-order total generalized variational model for Gaussian noise removal. By fusing an edge indicator function into the regularization term of the second-order total generalized variational model to guide the diffusion of gradients, our method aims to use the first or second derivative to enhance the intensity of the diffusion tensor. We use the first-order primal–dual algorithm to minimize the proposed energy function and achieve high-quality denoising and edge preserving result for depth maps with high -intensity noise. Extensive quantitative and qualitative evaluations in comparison to bench-mark datasets show that the proposed method provides significant higher accuracy and visual improvements than many state-of-the-art denoising algorithms.

Local reverse entropy weighted LBF model solving by Split Bregman for image segmentation

In this paper, an efficient level set model is proposed for image segmentation. Firstly, the original local binary fitting (LBF) model is redefined as a weighted energy integral, whose weight coefficient is the fast local reverse entropy of the image, and the total energy functional is then incorporated into a variational level set formulation. Secondly, the global convex segmentation method is used to construct a simplified convex segmentation model, at the same time, the edge information obtained by an edge indicator function is embedded into the total variation norm to further enhance the model’s target capture capability. Thirdly, the Split Bregman method is introduced to solve the generated convex optimization problem. Experimental results on synthetic and real images demonstrate that the proposed model has considerable improvements in terms of quantitative evaluation (being verified on the complete PASCAL VOC 2012 dataset), convergence rate, sensitivity to initial contour and robustness to noise interference compared with the state-of-the-art models. We also compare the proposed model with the famous FCN and Mask R-CNN, and make a special analysis on the adaptability of our method to occluded targets.

An integrated two-stage approach for image segmentation via active contours

A novel integrated two-stage approach is proposed for image segmentation, where the edge, global and local region information of images are in turn incorporated to define the intensity fitting energy. In the first stage, the Chan-Vese model flexibly assimilates the edge indicator function in the beginning, and then the Laplace operator is introduced to regularize the level set function when minimizing the energy functional. As an edge-based and global region-based active contour, it can be inclined to rapidly produce a coarse segmentation result. In the second stage, we further segment the image by absorbing the local region fitting energy, where its initialization is acquired by the final active contour of the first stage. In addition, we present a generalized level set regularization term, which efficiently eliminates the periodically re-initialization procedure of traditional level set methods and maintains the corresponding signed distance property. Compared with the first stage, the local object details are accurately segmented in the second stage, which can acquire an accurate segmentation result. Qualitative and quantitative experimental results demonstrate the accuracy, robustness and efficiency of our approach with applications to some synthetical and real-world images.

The application of gray-scale level-set method in segmentation of concrete deck delamination using infrared images

Conventional nondestructive delamination detection of concrete pavements through thermography is often based on temperature contrasts between delaminated and sound areas. Non-uniform backgrounds caused by the environmental conditions are often challenging for contrast-based methods to robustly differentiate the delaminated areas from the sound areas. Instead of focusing on the temperature contrast, this study proposes a temperature gradient-based level set method (LSM) to detect boundaries for delamination segmentations. A modified edge indicator function is developed to represent the normalized temperature gradient of a thermal image. The experimental study was conducted to evaluate its applicability and stability for boundary detection in terms of different burial depths and observation time windows. Then the LSM generated edges LSM were used for delamination segmentations. The results demonstrated significant improvements compared to the well-accepted k-mean method in terms of accuracy and stability of the detections. A field implementation of this method using an in-service bridge generated satisfactory outcomes when compared to the ground truth data. Major limitations and future works are also discussed in terms of parameter selections.

Active contour model based on improved fuzzy c-means algorithm and adaptive functions

Distance regularized level set evolution (DRLSE) model, which solves the re-initialization problem in early active contours, is a ground breaking edge-based model for image segmentation. However, it has the disadvantages of unsatisfactory robustness to initialization and noise, unidirectional movement, slow convergence and poor stability. In this paper, we propose an active contour model driven by improved fuzzy c-means algorithm (FCM) and adaptive functions. An adaptive sign function based on image clustering information not only increases stability, but also solves the problem of unidirectional movement. Furthermore, it gives our model the ability to selectively segment targets in image. An adaptive edge indicator function accelerates convergence with better function performance. To further increase stability, a novel double-well potential function and the corresponding evolution speed function are proposed. Due to the improved FCM, the proposed model is robust to initialization and noise. In addition, our model exhibits an edge-based and region-based characteristic. Experimental results have proved that the proposed model can not only effectively segment images with intensity inhomogeneity, but also show a good robustness to initialization. Moreover, it has shorter time spent and higher segmentation accuracy compared with other models.

Sinogram restoration for low-dose X-ray computed tomography using regularized Perona–Malik equation with intuitionistic fuzzy entropy

Edges and flat areas in the sinogram of low-dose X-ray computed tomography are difficult to distinguish. This lack of distinction leads to excessive smoothing in the sinogram restoration. To address this problem, we propose a sinogram restoration algorithm using the regularized Perona–Malik (P–M) equation with intuitionistic fuzzy entropy. Firstly, considering the sinogram fuzziness, a novel edge indicator function is constructed using both the gradient magnitude and intuitionistic fuzzy entropy. Secondly, using the constructed edge indicator function as the diffusion coefficient, a novel regularized P–M equation smoothing model is presented. The proposed model overcomes the shortage of traditional P–M equations, which are ill-conditioned. Moreover, it performs diffusion with different directions and intensities in different regions of the sinogram. The optimal solution of the proposed algorithm is obtained by using the additional operator splitting method. Finally, the reconstructed image is achieved by filtered back projection from the smoothed sinogram. Experimental results show that the presented method can retain important edges while smoothing noise and perform better than others.

Active contours driven by adaptive functions and fuzzy c-means energy for fast image segmentation

The shortcoming of geometric active contours is that they are extremely sensitive to positions of initialization. Initial contours of the distance regularized level set evolution model must be set inside or outside target completely. In addition, the model is prone to problems of falling into false boundary, leaking from weak edge and poor anti-noise ability. In this paper, we propose a robust active contour model driven by adaptive functions (including an adaptive edge indicator function and adaptive sign function) and fuzzy c-means energy. Utilize the adaptive edge indicator function which is composed of image intensity information to substitute traditional edge indicator function in the area term. Active contours can expand or shrink from initialization automatically, which improves the disadvantages of poor robustness to initialization and unidirectional movement. Due to the adaptive sign function and fuzzy c-means energy, the problems of slow convergence and leaking from weak edge have been solved. Moreover, a novel distance regularized term (mainly a potential function and evolution speed function) is proposed to make evolution more stable. Experimental results have proved that our model can segment images with intensity inhomogeneity effectively. Compared with other classic models, the proposed model not only shortens time spent and improves segmentation accuracy, but also shows a better robustness to initialization.

Local edge-enhanced active contour for accurate skin lesion border detection

BackgroundDermoscopy is one of the common and effective imaging techniques in diagnosis of skin cancer, especially for pigmented lesions. Accurate skin lesion border detection is the key to extract important dermoscopic features of the skin lesion. In current clinical settings, border delineation is performed manually by dermatologists. Operator based assessments lead to intra- and inter-observer variations due to its subjective nature. Moreover it is a tedious process. Because of aforementioned hurdles, the automation of lesion boundary detection in dermoscopic images is necessary. In this study, we address this problem by developing a novel skin lesion border detection method with a robust edge indicator function, which is based on a meshless method.ResultOur results are compared with the other image segmentation methods. Our skin lesion border detection algorithm outperforms other state-of-the-art methods. Based on dermatologist drawn ground truth skin lesion borders, the results indicate that our method generates reasonable boundaries than other prominent methods having Dice score of 0.886 ±0.094 and Jaccard score of 0.807 ±0.133.ConclusionWe prove that smoothed particle hydrodynamic (SPH) kernels can be used as edge features in active contours segmentation and probability map can be employed to avoid the evolving contour from leaking into the object of interest.

Image denoising via a new anisotropic total-variation-based model

To keep local structures when denoising the degraded image, we propose a new anisotropic total variation (TV)-based restored model based on the combination of the gradient operator ∇ and the adaptive weighted matrix ,T into the ℓ1-norm regularized term. The weighted matrix ,T depends on the edge indicator function along the x and y-axis directions, so this matrix can rotate the direction of the gradient operator tending to bigger weight and the proposed model can thus describe the local features in image. In order to cope with this nonsmooth model, we employ the alternating direction method of multipliers (ADMM) to solve it. Relying on the convexity, the convergence of the proposed numerical algorithm is provided as well. Denoising experiments on the artificial images and benchmark images show the effectiveness of the proposed model by comparing it to other well-known total-variation-based models in terms of the restored quality.

PET-MRI joint reconstruction with common edge weighted total variation regularization

Driven by recent developments of PET-MRI scanners, simultaneous reconstruction of dual-modality has gained considerable research interest. The purpose of this paper is to propose a joint reconstruction model by utilizing complementary information of dual-modality to improve reconstruction quality of individual images. We propose a total variation based joint regularization with an adaptively estimated common edge indicator function as a weight. The common edge function takes into account the shared structures of two modalities in a flexible way. A proximal alternating algorithm is adopted to recover dual-modality images and the common edge, and the convergence of the overall numerical scheme is established. Finally, numerical tests for PET and MRI under different noise levels and subsampling patterns show that the proposed approach obtains favorable results compared to some existing methods.

Color Transfer Using Adaptive Second-Order Total Generalized Variation Regularizer

Color transfer is to generate synthetic images by changing the color of target images with new colors obtained from given source images, while the geometrical structure of the synthetic images remains the same. Classical color transfer models use a total variation (TV) regularizer to preserve the details and suppress the noise of the synthetic images. These models can sometimes cause staircase effect and geometrical structure details over-smoothed. To overcome these problems, we propose a new color transfer model in which an adaptive second-order total generalized variation (TGV) regularizer is designed. Here, the adaptive second-order TGV regularizer is a weighted second-order TGV regularizer. The weight is computed by an adaptive edge indicator function. In addition, an efficient algorithm is developed to program our new model. The algorithm is based on a weighted primal–dual method. Experimental results and comparisons demonstrate that our new color transfer model can generate better results than classical TV regularizer-based models in the aspects of the inhibition of staircase effect and the preservation of image details.

An adaptive level set method for improving image segmentation

Segmentation is one of the most significant techniques in image processing studies. But the major limitations of low contrast, ambiguous boundary and complex morphology of images usually lead to unsatisfactory segmentation, especially in heavily noisy medical images. To address this problem, an attempt by improving Distance Regularized Level Set Evolution (DRLSE) model has been made to build up an effective and accurate active contour model to improve the segmentation ability. In this study, a balance concept between the pushing force and image’s contour strength of DRLSE model was adapted for contour segmentations, so the contour convergent/divergent force will be re-defined to make it more feasible for complicated boundaries. The proposed concept integrates the bilateral filtering and Canny contour, and the improved edge indicator function into the DRLSE model. The most important step is to adapt the improved edge indicator function appropriately with the Canny contour. To verify our proposed DRLSE scheme, different testing images are used. The experimental results show that the proposed approach has been examined and tested successfully in most cases. Consequently, the developed algorithm including the DRLSE model combing the Canny contour with an improved g edge indicator, demonstrate the effectiveness and reliability, especially in the testing samples with weak edges and complex topologies.

Thermal Infrared Pedestrian Image Segmentation Using Level Set Method.

The edge-based active contour model has been one of the most influential models in image segmentation, in which the level set method is usually used to minimize the active contour energy function and then find the desired contour. However, for infrared thermal pedestrian images, the traditional level set-based method that utilizes the gradient information as edge indicator function fails to provide the satisfactory boundary of the target. That is due to the poorly defined boundaries and the intensity inhomogeneity. Therefore, we propose a novel level set-based thermal infrared image segmentation method that is able to deal with the above problems. Specifically, we firstly explore the one-bit transform convolution kernel and define a soft mark, from which the target boundary is enhanced. Then we propose a weight function to adaptively adjust the intensity of the infrared image so as to reduce the intensity inhomogeneity. In the level set formulation, those processes can adaptively adjust the edge indicator function, from which the evolving curve will stop at the target boundary. We conduct the experiments on benchmark infrared pedestrian images and compare our introduced method with the state-of-the-art approaches to demonstrate the excellent performance of the proposed method.