text: Verifying an identity claim by fingerprint recognition is a commonplace experience for millions of people in their daily life, for example, for unlocking a tablet computer or smartphone. The first processing step after fingerprint image acquisition is segmentation, that is, dividing a fingerprint image into a foreground region which contains the relevant features for the comparison algorithm, and a background region. The authors propose a novel segmentation method by global three-part decomposition (G3PD). On the basis of global variational analysis, the G3PD method decomposes a fingerprint image into cartoon, texture and noise parts. After decomposition, the foreground region is obtained from the non-zero coefficients in the texture image using morphological processing. The segmentation performance of the G3PD method is compared with five state-of-the-art methods on a benchmark which comprises manually marked ground truth segmentation for 10,560 images. Performance evaluations show that the G3PD method consistently outperforms existing methods in terms of segmentation accuracy.
  @cite_61: 
  @cite_14: We propose a new model for active contours to detect objects in a given image, based on techniques of curve evolution, Mumford-Shah (1989) functional for segmentation and level sets. Our model can detect objects whose boundaries are not necessarily defined by the gradient. We minimize an energy which can be seen as a particular case of the minimal partition problem. In the level set formulation, the problem becomes a "mean-curvature flow"-like evolving the active contour, which will stop on the desired boundary. However, the stopping term does not depend on the gradient of the image, as in the classical active contour models, but is instead related to a particular segmentation of the image. We give a numerical algorithm using finite differences. Finally, we present various experimental results and in particular some examples for which the classical snakes methods based on the gradient are not applicable. Also, the initial curve can be anywhere in the image, and interior contours are automatically detected.
  @cite_15: In this paper, we present an efficient approach for unsupervised segmenta- tion of natural and textural images based on the extraction o fi mage features and a fast active contour segmentation model. We address the problem of textures where neither the gray-level information nor the boundary information is adequate for object extraction. This is often the case of natural images compose do f both homogeneous and textured regions. Because these images cannot be in generaldirectly processed by the gray-level information, we propose a new texture descripto rw hich intrinsically def ines the geometry of textures using semi-local image informatio na nd tools from differen- tial geometry. Then, we use the popular Kullback-Leibler distance to design an active contour model which distinguishes the background and textures of interest. The exis- tence of a minimizing solution to the proposed segmentationmodel is proven. Finally, at exture segmentation algorithm based on the Split-Bregma nm ethod is introduced to extract meaningful objects in a fast way. Promising synthetic and real-world results for gray-scale and color images are presented.
  @cite_28: Fingerprint recognition plays an important role in many commercial applications and is used by millions of people every day, e.g. for unlocking mobile phones. Fingerprint image segmentation is typically the first processing step of most fingerprint algorithms and it divides an image into foreground, the region of interest, and background. Two types of error can occur during this step which both have a negative impact on the recognition performance: ‘true’ foreground can be labeled as background and features like minutiae can be lost, or conversely ‘true’ background can be misclassified as foreground and spurious features can be introduced. The contribution of this paper is threefold: firstly, we propose a novel factorized directional bandpass (FDB) segmentation method for texture extraction based on the directional Hilbert transform of a Butterworth bandpass (DHBB) filter interwoven with soft-thresholding. Secondly, we provide a manually marked ground truth segmentation for 10560 images as an evaluation benchmark. Thirdly, we conduct a systematic performance comparison between the FDB method and four of the most often cited fingerprint segmentation algorithms showing that the FDB segmentation method clearly outperforms these four widely used methods. The benchmark and the implementation of the FDB method are made publicly available.
  @cite_53: Image segmentation is an important and fundamental task in many digital image processing systems. Image segmentation by thresholding is the simplest technique and involves the basic assumption that objects and background in the digital image have distinct gray-level distributions. In this paper, we present a general technique for thresholding of digital images based on Renyi's entropy. Our method includes two of the previously proposed well known global thresholding methods. The effectiveness of the proposed method is demonstrated by using examples from the real-world and synthetic images.
  @cite_40: We show how certain nonconvex optimization problems that arise in image processing and computer vision can be restated as convex minimization problems. This allows, in particular, the finding of global minimizers via standard convex minimization schemes.
  @cite_59: The active contour snake model is one of the most successful variational models in image segmentation. It consists of evolving a contour in images toward the boundaries of objects. Its success is based on strong mathematical properties and efficient numerical schemes based on the level set method. The only drawback of this model is the existence of local minima in the active contour energy, which makes the initial guess critical to get satisfactory results. In this paper, we propose to solve this problem by determining a global minimum of the active contour model. Our approach is based on the unification of image segmentation and image denoising tasks into a global minimization framework. More precisely, we propose to unify three well-known image variational models, namely the snake model, the Rudin---Osher---Fatemi denoising model and the Mumford---Shah segmentation model. We will establish theorems with proofs to determine the existence of a global minimum of the active contour model. From a numerical point of view, we propose a new practical way to solve the active contour propagation problem toward object boundaries through a dual formulation of the minimization problem. The dual formulation, easy to implement, allows us a fast global minimization of the snake energy. It avoids the usual drawback in the level set approach that consists of initializing the active contour in a distance function and re-initializing it periodically during the evolution, which is time-consuming. We apply our segmentation algorithms on synthetic and real-world images, such as texture images and medical images, to emphasize the performances of our model compared with other segmentation models.
  @cite_63: We address the issue of textured image segmentation in the context of the Gabor feature space of images. Gabor filters tuned to a set of orientations, scales and frequencies are applied to the images to create the Gabor feature space. A two-dimensional Riemannian manifold of local features is extracted via the Beltrami framework. The metric of this surface provides a good indicator of texture changes and is used, therefore, in a Beltrami-based diffusion mechanism and in a geodesic active contours algorithm for texture segmentation. The performance of the proposed algorithm is compared with that of the edgeless active contours algorithm applied for texture segmentation. Moreover, an integrated approach, extending the geodesic and edgeless active contours approaches to texture segmentation, is presented. We show that combining boundary and region information yields more robust and accurate texture segmentation results.
  @cite_46: In this paper, we propose a PDE-based level set method. Traditionally, interfaces are represented by the zero level set of continuous level set functions. Instead, we let the interfaces be represented by discontinuities of piecewise constant level set functions. Each level set function can at convergence only take two values, i.e., it can only be 1 or -1; thus, our method is related to phase-field methods. Some of the properties of standard level set methods are preserved in the proposed method, while others are not. Using this new method for interface problems, we need to minimize a smooth convex functional under a quadratic constraint. The level set functions are discontinuous at convergence, but the minimization functional is smooth. We show numerical results using the method for segmentation of digital images.
  @cite_13: Image analysis usually refers to processing of images with the goal of finding objects presented in the image. Image segmentation is one of the most critical tasks in automatic image analysis. The nonextensive entropy is a recent development in statistical mechanics and it is a new formalism in which a real quantity q was introduced as parameter for physical systems that present long range interactions, long time memories and fractal-type structures. In image processing, one of the most efficient techniques for image segmentation is entropy-based thresholding. This approach uses the Shannon entropy originated from the information theory considering the gray level image histogram as a probability distribution. In this paper, Tsallis entropy is applied as a general entropy formalism for information theory. For the first time image thresholding by nonextensive entropy is proposed regarding the presence of nonadditive information content in some image classes. Some typical results are presented to illustrate the influence of the parameter q in the thresholding.
summary: With more than hundred methods, we refer the reader to @cite_28 for an overview over the literature of fingerprint segmentation methods. For image segmentation in general, there is a plethora of approaches to solve this problem. These are based e.g. on the intensity of pixels @cite_61 , @cite_53 , @cite_13 , or the evolution of curves for piecewise smooth regions in images @cite_14 , @cite_59 , @cite_40 , @cite_46 . Texture segmentation, however, is still an open problem, because intensity values are inadequate, e.g. for segmenting fingerprint patterns. Methods based on texture descriptors @cite_63 , @cite_15 or finding other meaningful features in an observed image for classification have been suggested.