Breast cancer is a frequent form of cancer for women, and globally it is a major cause of death. Early detection is crucial for effective diagnosis and treatment, and can also help to lower mortality rates. In recent years, Convolutional Neural Networks have been applied to mammography to assist radiologists improve their efficiency and precision. U-Net is a fully convolutional neural network and a popular model that uses the encoder-decoder architecture, it is known for its capacity to effectively segment biomedical images. This work aims to present a new model for breast cancer detection and segmentation. Our first purpose was to discover a reliable segmentation model for breast masses in mammography images by combining the ResNet architecture and U-Net. Subsequently, we trained several standard models for classification in normal and abnormal images, such as ResNet101, ResNet152, DenseNet169, MobileNet, InceptionV3, and NasNet. Furthermore, based on the segmentation model that yielded good experimental results, we created our classification model by modifying the output layers in order to generate a prediction label (Normal or Abnormal) instead of generating a mask. Our study contributes to the field of breast cancer detection by employing a novel approach that performs detection and segmentation directly on the entire mammography image, unlike traditional methods that operate on image patches. The main advantage of the proposed approach is to simplify the workflow of breast masses segmentation by eliminating intermediate steps which can introduce errors and increase the complexity of the system. Furthermore, our approach focuses on reducing false positives, which are a common challenge in breast cancer detection. Our classification model reached better results compared to other experimented classification models. We used the INbreast dataset of mammography images to train and evaluate our models. In addition to that we employed GradCAM in order to visualize the prediction results and to have an interpretation of the results.

This paper investigates a convex-relaxed kernel mapping formulation of image segmentation. We optimize, under some partition constraints, a functional containing two characteristic terms: 1) a data term, which maps the observation space to a higher (possibly infinite) dimensional feature space via a kernel function, thereby evaluating nonlinear distances between the observations and segments parameters and 2) a total-variation term, which favors smooth segment surfaces (or boundaries). The algorithm iterates two steps: 1) a convex-relaxation optimization with respect to the segments by solving an equivalent constrained problem via the augmented Lagrange multiplier method and 2) a convergent fixed-point optimization with respect to the segments parameters. The proposed algorithm can bear with a variety of image types without the need for complex and application-specific statistical modeling, while having the computational benefits of convex relaxation. Our solution is amenable to parallelized implementations on graphics processing units (GPUs) and extends easily to high dimensions. We evaluated the proposed algorithm with several sets of comprehensive experiments and comparisons, including: 1) computational evaluations over 3D medical-imaging examples and high-resolution large-size color photographs, which demonstrate that a parallelized implementation of the proposed method run on a GPU can bring a significant speed-up and 2) accuracy evaluations against five state-of-the-art methods over the Berkeley color-image database and a multimodel synthetic data set, which demonstrates competitive performances of the algorithm.

This study proposes a novel multiregion image segmentation method using convex relaxation optimization and kernel mapping of the image data. The image data is transformed by a kernel function in order to support various image models while avoiding complex modeling. This is embedded implicitly in an objective function which is optimized by iterating a two-step strategy. First, a fixed point sequence is used to evaluate the regions parameters. Second, the image partition is updated by an efficient multiplier-based algorithm which uses the standard augmented Lagrangian method. A thorough experimental study is carried out over a multi-model synthetic dataset, the Berkeley database, as well as cardiac 3D data to show the effectiveness of the proposed method.

This study investigates the recovery of region boundary patterns in an image by a variational level set method which drives an active curve to coincide with boundaries on which a feature distribution matches a reference distribution. We formulate the scheme for both the Kullback-Leibler and the Bhattacharyya similarities, and apply it in two conditions: the simultaneous recovery of all region boundaries consistent with a given outline pattern, and segmentation in the presence of faded boundary segments. The first task uses an image-based geometric feature, and the second a photometric feature. In each case, the corresponding curve evolution equation can be viewed as a geodesic active contour (GAC) flow having a variable stopping function which depends on the feature distribution on the active curve. This affords a potent global representation of the target boundaries, which can effectively drive active curve segmentation in a variety of otherwise adverse conditions. Detailed experimentation shows that the scheme can significantly improve on current region and edge-based formulations.

Road network extraction from digitized map consists in partitioning a map into two different classes (road and background) distinguished with their intensity values and geometric shape. In this paper, we propose a semi-automatic method where user intervention is minimal. We adopt a variational framework where a minimization energy is proposed. Roads are tracked by active contours which evolve according to evolution equations derived from the energy minimization. We consider that the energy is composed of three main terms which have never been combined and used in such application. The first term is the geodesic active contour (GAC) which is contour-based and which evolves toward high gradients in the image. The second term matches the intensity distribution inside the contour with a model distribution. The third term is a geometric constraint which describes the thin structure of routes. The user intervention is restricted to learning the road intensity model.

The purpose of this study is to investigate multiregion graph cut image partitioning via kernel mapping of the image data. The image data is transformed implicitly by a kernel function so that the piecewise constant model of the graph cut formulation becomes applicable. The objective function contains an original data term to evaluate the deviation of the transformed data, within each segmentation region, from the piecewise constant model, and a smoothness, boundary preserving regularization term. The method affords an effective alternative to complex modeling of the original image data while taking advantage of the computational benefits of graph cuts. Using a common kernel function, energy minimization typically consists of iterating image partitioning by graph cut iterations and evaluations of region parameters via fixed point computation. A quantitative and comparative performance assessment is carried out over a large number of experiments using synthetic grey level data as well as natural images from the Berkeley database. The effectiveness of the method is also demonstrated through a set of experiments with real images of a variety of types such as medical, synthetic aperture radar, and motion maps.

This study investigates an active curve functional which measures a similarity between the distribution of an image feature on the curve and a model distribution learned a priori. The curve evolution equation resulting from the minimization of this contour-based functional can be viewed as a geodesic active contour with a variable stopping function. The variable stopping function depends on the distribution of image feature on the curve and, therefore, can deal with difficult cases where the desired boundary corresponds to very weak image transitions. We ran several experiments supported by quantitative performance evaluations over several examples of segmentation and tracking of the left ventricle inner and outer boundaries in cardiac magnetic resonance image sequences. The results are significantly more accurate than with region-based and edge-based functionals.

A novel multiregion graph cut image partitioning method combined with kernel mapping is presented. A kernel function transforms implicitly the image data into data of a higher dimension so that the piecewise constant model of the graph cut formulation becomes applicable. The method yields an effective alternative to complex modeling of the original image data while taking advantage of the rapidity of graph cuts. A variety of noise models are, thus, considered by a single model. Using a common kernel function, we minimize the objective functional by iterating (1) regions parameters update and (2) image partitioning by graph cut iterations. A comparative performance evaluation is carried out over a large set of experiments using synthetic grey level data. Besides, a set of tests with real images such as SAR and medical images is shown to demonstrate the validity of the method.

This study investigates level set multiphase image segmentation by kernel mapping and piecewise constant modeling of the image data thereof. A kernel function maps implicitly the original data into data of a higher dimension so that the piecewise constant model becomes applicable. This leads to a flexible and effective alternative to complex modeling of the image data. The method uses an active curve objective functional with two terms: an original term which evaluates the deviation of the mapped image data within each segmentation region from the piecewise constant model and a classic length regularization term for smooth region boundaries. Functional minimization is carried out by iterations of two consecutive steps: 1) minimization with respect to the segmentation by curve evolution via Euler-Lagrange descent equations and 2) minimization with respect to the regions parameters via fixed point iterations. Using a common kernel function, this step amounts to a mean shift parameter update. We verified the effectiveness of the method by a quantitative and comparative performance evaluation over a large number of experiments on synthetic images, as well as experiments with a variety of real images such as medical, satellite, and natural images, as well as motion maps.

A novel level set multiphase image segmentation method combined with kernel mapping is presented. A kernel function maps implicitly the original data into data of a higher dimension so that the piecewise constant model becomes applicable. The goal is to consider several types of noise by a single model. Gradient flow equations are iteratively derived in order to minimize the segmentation functional with respect to the partition, in a first step, and the regions parameters in a second step. Using a common kernel function, we verified the effectiveness of the method by a quantitative and comparative performance evaluation over experiments on synthetic images, as well as a variety of real images such as medical, SAR, and natural images.