Additive Operator Splitting Scheme Research Articles

Enhanced Deep Learning Architectures for Face Liveness Detection for Static and Video Sequences.

Face liveness detection is a critical preprocessing step in face recognition for avoiding face spoofing attacks, where an impostor can impersonate a valid user for authentication. While considerable research has been recently done in improving the accuracy of face liveness detection, the best current approaches use a two-step process of first applying non-linear anisotropic diffusion to the incoming image and then using a deep network for final liveness decision. Such an approach is not viable for real-time face liveness detection. We develop two end-to-end real-time solutions where nonlinear anisotropic diffusion based on an additive operator splitting scheme is first applied to an incoming static image, which enhances the edges and surface texture, and preserves the boundary locations in the real image. The diffused image is then forwarded to a pre-trained Specialized Convolutional Neural Network (SCNN) and the Inception network version 4, which identify the complex and deep features for face liveness classification. We evaluate the performance of our integrated approach using the SCNN and Inception v4 on the Replay-Attack dataset and Replay-Mobile dataset. The entire architecture is created in such a manner that, once trained, the face liveness detection can be accomplished in real-time. We achieve promising results of 96.03% and 96.21% face liveness detection accuracy with the SCNN, and 94.77% and 95.53% accuracy with the Inception v4, on the Replay-Attack, and Replay-Mobile datasets, respectively. We also develop a novel deep architecture for face liveness detection on video frames that uses the diffusion of images followed by a deep Convolutional Neural Network (CNN) and a Long Short-Term Memory (LSTM) to classify the video sequence as real or fake. Even though the use of CNN followed by LSTM is not new, combining it with diffusion (that has proven to be the best approach for single image liveness detection) is novel. Performance evaluation of our architecture on the REPLAY-ATTACK dataset gave 98.71% test accuracy and 2.77% Half Total Error Rate (HTER), and on the REPLAY-MOBILE dataset gave 95.41% accuracy and 5.28% HTER.

Optimizing Deep CNN Architectures for Face Liveness Detection.

Face recognition is a popular and efficient form of biometric authentication used in many software applications. One drawback of this technique is that it is prone to face spoofing attacks, where an impostor can gain access to the system by presenting a photograph of a valid user to the sensor. Thus, face liveness detection is a necessary step before granting authentication to the user. In this paper, we have developed deep architectures for face liveness detection that use a combination of texture analysis and a convolutional neural network (CNN) to classify the captured image as real or fake. Our development greatly improved upon a recent approach that applies nonlinear diffusion based on an additive operator splitting scheme and a tridiagonal matrix block-solver algorithm to the image, which enhances the edges and surface texture in the real image. We then fed the diffused image to a deep CNN to identify the complex and deep features for classification. We obtained 100% accuracy on the NUAA Photograph Impostor dataset for face liveness detection using one of our enhanced architectures. Further, we gained insight into the enhancement of the face liveness detection architecture by evaluating three different deep architectures, which included deep CNN, residual network, and the inception network version 4. We evaluated the performance of each of these architectures on the NUAA dataset and present here the experimental results showing under what conditions an architecture would be better suited for face liveness detection. While the residual network gave us competitive results, the inception network version 4 produced the optimal accuracy of 100% in liveness detection (with nonlinear anisotropic diffused images with a smoothness parameter of 15). Our approach outperformed all current state-of-the-art methods.

Fast Von Mises strain imaging on ultrasound carotid vessel wall by flow driven diffusion method.

The elasticity of the vessel wall is important for the clinical identification of rupture-risks. The Von Mises strain can be a potential index for the indication of carotid vessel pathologies. In this paper, a fast clinically applicable real-time algorithm from time-sequence of B-mode carotid images is developed. Due to the compression induced by the normal cardiac pulsation, tissue motion occurs radially and non-rigidly. To obtain an accurate motion field, we developed a variational functional integrating the optical flow equation and an anisotropic regularizer, and designed a diffusion tensor to encourage coherence diffusion. The motion field is smoothed along the desired motion flow orientation. A fast, additive operator splitting scheme, which is ten times faster than the conventional discrete method, is used for the numerical implementation. To demonstrate the efficiency of the proposed approach, finite element models are set up for normal and pathological carotid vessel walls. The results indicate that the proposed diffusion approach obtains an accurate smooth and continuous motion field and greatly improves the follow up strain estimation using a fast differential strain filter. Furthermore, our approach using the Von Mises strain imaging on clinical ultrasound images of the carotid artery is validated. Participants above 65-years in age suffering from different stages of atherosclerosis in their carotid artery are selected. The results are evaluated by an experienced physician. The evaluation results demonstrate that the Von Mises strain has a good correspondence to the presence of certain suspicious areas in the B-mode images. The proposed method is therefore clinically applicable for the real-time Von Mises strain imaging of carotid vessel walls, and can be of great value as a complementary method to B-mode image for the clinical identification of the risk of plaque vulnerability.

Deep face liveness detection based on nonlinear diffusion using convolution neural network

A face-spoofing attack occurs when an imposter manipulates a face recognition and verification system to gain access as a legitimate user by presenting a 2D printed image or recorded video to the face sensor. This paper presents an efficient and non-intrusive method to counter face-spoofing attacks that uses a single image to detect spoofing attacks. We apply a nonlinear diffusion based on an additive operator splitting scheme. Additionally, we propose a specialized deep convolution neural network that can extract the discriminative and high-level features of the input diffused image to differentiate between a fake face and a real face. Our proposed method is both efficient and convenient compared with the previously implemented state-of-the-art methods described in the literature review. We achieved the highest reported accuracy of 99% on the widely used NUAA dataset. In addition, we tested our method on the Replay Attack dataset which consists of 1200 short videos of both real access and spoofing attacks. An extensive experimental analysis was conducted that demonstrated better results when compared to previous static algorithms results. However, this result can be improved by applying a sparse autoencoder learning algorithm to obtain a more distinguishable diffused image.

Hybrid level set method based on image diffusion

In this paper, a new hybrid diffusion-based level set method is proposed to efficiently address the complex image segmentation problem. Different from the traditional methods, the proposed method is performed on image diffusion space rather than intensity space. Firstly, the nonlinear diffusion based on total variation flow and additive operator splitting scheme is performed on the original intensity image to obtain the diffused image. Then, the local diffusion energy term is constructed by performing homomorphic unsharp masking operation on diffused image so as to implement a local piecewise constant search. To avoid trapping into local minimum produced by local energy, the global diffusion energy term is formed by approximating diffused image in a global piecewise constant way. Besides, the regularization energy term is included to have penalization effect on evolving contour length and maintenance of level set function being signed distance function. By minimizing the overall energy functional which is a linear combination of local energy, global energy and regularization energy, the evolving contour can be driven to approach the object boundary. The experiments on different characteristics of complex images have shown that the proposed method can achieve satisfying segmentation performance accompanied with some good properties, i.e. the robustness to initial parameter and contour setting, noise insensitivity, quick and stable convergence.

Active contour-based colour image selective segmentation

This paper proposes an active contour-based selective segmentation model for colour images. This model combines region information with edge detection, taking advantages of two models, that is, a region-based model that doesn't rely on image gradient, and an edge-based model that can produce a satisfactory segmentation result for inhomogeneous areas. This model calculates colour image edge by treating a colour image as a whole, instead of treating it separately. It overcomes the shortcoming of no uniform result. The Euler-Lagrange equation can be quickly solved by the additive operator splitting scheme. Besides, we need give several points near the boundary of the interested region, and then the edge detection function and distance function can help stop the active contour evolution. The segmentation results show the validity and the robustness of the proposed model.

Structural topology optimization using an enhanced level set method

This paper proposes an effective algorithm based on the Level Set Method (LSM) to solve the problem of topology optimization. The Hamilton–Jacobi Partial Differential Equation (H-J PDE), level set equation, is modified to increase the performance. We combine the topological derivative with nonlinear LSM to create a remedy against premature convergence and strong dependency of the optimal topology on the initial design. The magnitude of the gradient in the LS equation was replaced by several Delta functions and the results were explored. Instead of the explicit scheme, which is commonly used in conventional LSM, a semi-implicit additive operator splitting scheme was carried out in our study to solve the LS equation. A truncation strategy was implemented to limit maximum and minimum values in the design domain. Finally, several numerical examples were provided to confirm the validity of the method and show its accuracy, as well as convergence speed.

Fast Iterative Algorithms for Total Variation Based Multiplicative Noise Removal Model

This paper presents fast iterative algorithms for solution of PDEs arisen from minimization of multiplicative noise removal model [14]. This model may be regarded as an improved version of the Total Variation (TV) de-noising models. For the TV and the multiplicative noise removal models, their associated Euler-Lagrange equations are highly nonlinear Partial Differential Equations (PDEs). For this model a very slow explicit time marching method has been reported. The main contribution we present in this paper is the implementation of the fixed point, semi-implicit and additive operator splitting schemes which do not yield good results. Consequently a fast and efficient multi-grid method with AOS as smoother is developed. Numerical experiments are presented to show the good performance of the fast multi-grid algorithm.

Complementary tensor-driven image coherence diffusion for oriented structure enhancement

Abstract Oriented structure enhancement plays important role in computer vision tasks, where the diffusion is encouraged along the preferred direction instead of perpendicular to it. By analyzing the differential geometric property of the oriented structure, a complementary tensor is proposed by combining the first and the second-order structure tensors as complementary descriptors, which can precisely analyze not only the step edges, but also the weak edges such as narrow peak or ridge-like structures. Complementary diffusion tensor is constructed from the new structure tensor, which steers coherence diffusion for oriented structure enhancement. Furthermore, fast algorithm based on additive operator splitting scheme is used for numerical solution, which is much faster than usual approach. The experimental results on several images are provided. Experiments show that the image diffusion process steered by the new complementary tensor can strengthen the oriented structures and also close the interrupted lines as well. Both strong and weak edges are enhanced while noise is removed. Our approach is very promising and could be applied to many other images.

New Variational Formulations for Level Set Evolution Without Reinitialization with Applications to Image Segmentation

Interface evolution problems are often solved elegantly by the level set method, which generally requires the time-consuming reinitialization process. In order to avoid reinitialization, we reformulate the variational model as a constrained optimization problem. Then we present an augmented Lagrangian method and a projection Lagrangian method to solve the constrained model and propose two gradient-type algorithms. For the augmented Lagrangian method, we employ the Uzawa scheme to update the Lagrange multiplier. For the projection Lagrangian method, we use the variable splitting technique and get an explicit expression for the Lagrange multiplier. We apply the two approaches to the Chan-Vese model and obtain two efficient alternating iterative algorithms based on the semi-implicit additive operator splitting scheme. Numerical results on various synthetic and real images are provided to compare our methods with two others, which demonstrate effectiveness and efficiency of our algorithms.

On the Acceleration of AOS Schemes for Nonlinear Diffusion Filtering

Based on the renowned additive operator splitting (AOS) schemes that ensure equal treatment of all coordinate axis, accelerated AOS schemes for solving regularized Perona-Malik (P-M) equation are presented. These ameliorated AOS schemes are stable unconditionally, consistent with nonlinear parabolic equations under certain circumstance and demonstrate a remarkably economical CPU time. The paper is intended to discuss the properties of the modified AOS schemes in several aspects. Finally, experiments show that as well as the edges and detailed information of images are preserved, the proposed AOS schemes are at least twice more efficient than the conventional AOS schemes.

Moving objects segmentation based on piecewise constant Mumford-Shah model solving by additive operator splitting

We propose a moving objects segmentation method for color image sequences based on the piecewise constant Mumford-Shah model (also known as the C-V model) solving by the semi-implicit additive operator splitting (AOS) scheme, which is unconditionally stable, fast, and easy to implement. The method first uses the Gaussian mixture model for background modeling and then subtracts the background to obtain the moving regions that are the handling objects of our method. As a result of the introduction of the AOS scheme, we could use a rather large time step and still maintain the stability of the evolution process. Additionally, the method can easily be parallelized because the AOS scheme decomposes the equations into a sequence of one-dimensional (1-D) systems. The experimental results demonstrate that under real moving objects video tests, the AOS scheme accelerates the evolution of the curve and significantly reduces the number of iterations, and also demonstrates the validity of our method.

Anisotropic Diffusion for Hyperspectral Imagery Enhancement

Among all enhancement techniques being developed over the past two decades, anisotropic diffusion has received much attention and experienced significant developments, with promising results and applications in various specific domains. The elegant property of the technique is that it can enhance images by reducing undesirable intensity variability within the objects in the image, while improving SNR and enhancing the contrast of the edges in scalar and, more recently, vector-valued images, such as color, multispectral, and hyperspectral imagery. In this paper, we present an alternative hyperspectral anisotropic diffusion scheme that takes into account the recent advances and the specificities of hyperspectral remote sensing. In addition, the proposed anisotropic diffusion algorithm can improve the classification accuracy of hyperspectral imagery by reducing the spatial and spectral variability of the image, while preserving the edges of objects. It is also revealed that the additive operator splitting scheme of our method can increase computer efficiency. Qualitative experiments, based on a real hyperspectral remote sensing image, show significant improvements in visual effects when using our method. Quantitative analyses, based on classification accuracies, confirm the superiority and validity of the proposed diffusion algorithm.

Geodesic active contour under geometrical conditions: theory and 3D applications

In this paper, we propose a new scheme for both detection of boundaries and fitting of geometrical data based on a geometrical partial differential equation, which allows a rigorous mathematical analysis. The model is a geodesic-active-contour-based model, in which we are trying to determine a curve that best approaches the given geometrical conditions (for instance a set of points or curves to approach) while detecting the object under consideration. Formal results concerning existence, uniqueness (viscosity solution) and stability are presented as well. We give the discretization of the method using an additive operator splitting scheme which is very efficient for this kind of problem. We also give 2D and 3D numerical examples on real data sets.

Unsupervised hierarchical image segmentation with level set and additive operator splitting

This paper presents an unsupervised hierarchical segmentation method for multi-phase images based on a single level set (2-phase) method and the semi-implicit additive operator splitting (AOS) scheme which is stable, fast, and easy to implement. The method successively segments image subregions found at each step of the hierarchy using a decision criterion based on the variance of intensity across the current subregion. The segmentation continues until a specified number of levels has been reached. The segmentation information for sub-images at each stage is stored in a tree data structure, and is used for reconstructing the segmented images. The method avoids the complicated governing equations of the multi-phase segmentation approach, and appears to converge in fewer iterations. The method can easily be parallelized because the AOS scheme decomposes the equations into a sequence of one dimensional systems.

Multiplicative Operator Splittings in Nonlinear Diffusion: From Spatial Splitting to Multiple Timesteps

Operator splitting is a powerful concept used in many diversed fields of applied mathematics for the design of effective numerical schemes. Following the success of the additive operator splitting (AOS) in performing an efficient nonlinear diffusion filtering on digital images, we analyze the possibility of using multiplicative operator splittings to process images from different perspectives. We start by examining the potential of using fractional step methods to design a multiplicative operator splitting as an alternative to AOS schemes. By means of a Strang splitting, we attempt to use numerical schemes that are known to be more accurate in linear diffusion processes and apply them on images. Initially we implement the Crank-Nicolson and DuFort-Frankel schemes to diffuse noisy signals in one dimension and devise a simple extrapolation that enables the Crank-Nicolson to be used with high accuracy on these signals. We then combine the Crank-Nicolson in 1D with various multiplicative operator splittings to process images. Based on these ideas we obtain some interesting results. However, from the practical standpoint, due to the computational expenses associated with these schemes and the questionable benefits in applying them to perform nonlinear diffusion filtering when using long timesteps, we conclude that AOS schemes are simple and efficient compared to these alternatives. We then examine the potential utility of using multiple timestep methods combined with AOS schemes, as means to expedite the diffusion process. These methods were developed for molecular dynamics applications and are used efficiently in biomolecular simulations. The idea is to split the forces exerted on atoms into different classes according to their behavior in time, and assign longer timesteps to nonlocal, slowly-varying forces such as the Coulomb and van der Waals interactions, whereas the local forces like bond and angle are treated with smaller timesteps. Multiple timestep integrators can be derived from the Trotter factorization, a decomposition that bears a strong resemblance to a Strang splitting. Both formulations decompose the time propagator into trilateral products to construct multiplicative operator splittings which are second order in time, with the possibility of extending the factorization to higher order expansions. While a Strang splitting is a decomposition across spatial dimensions, where each dimension is subsequently treated with a fractional step, the multiple timestep method is a decomposition across scales. Thus, multiple timestep methods are a realization of the multiplicative operator splitting idea. For certain nonlinear diffusion coefficients with favorable properties, we show that a simple multiple timestep method can improve the diffusion process.

Efficient image segmentation using partial differential equations and morphology

The goal of this paper is to investigate segmentation methods that combine fast preprocessing algorithms using partial differential equations (PDEs) with a watershed transformation with region merging. We consider two well-founded PDE methods: a nonlinear isotropic diffusion filter that permits edge enhancement, and a convex nonquadratic variational image restoration method which gives good denoising. For the diffusion filter, an efficient algorithm is applied using an additive operator splitting (AOS) that leads to recursive and separable filters. For the variational restoration method, a novel algorithm is developed that uses AOS schemes within a Gaussian pyramid decomposition. Examples demonstrate that preprocessing by these PDE techniques significantly improves the watershed segmentation, and that the resulting segmentation method gives better results than some traditional techniques. The algorithm has linear complexity and it can be used for arbitrary dimensional data sets. The typical CPU time for segmenting a 256 2 image on a modern PC is far below 1 s.

Efficient and reliable schemes for nonlinear diffusion filtering

Nonlinear diffusion filtering in image processing is usually performed with explicit schemes. They are only stable for very small time steps, which leads to poor efficiency and limits their practical use. Based on a discrete nonlinear diffusion scale-space framework we present semi-implicit schemes which are stable for all time steps. These novel schemes use an additive operator splitting (AOS), which guarantees equal treatment of all coordinate axes. They can be implemented easily in arbitrary dimensions, have good rotational invariance and reveal a computational complexity and memory requirement which is linear in the number of pixels. Examples demonstrate that, under typical accuracy requirements, AOS schemes are at least ten times more efficient than the widely used explicit schemes.