A scheme is developed for classifying the types of motion perceived by a humanlike robot. It is assumed that the robot receives visual images of the scene using a perspective system model. Equations, theorems, concepts, clues, etc., relating the objects, their positions, and their motion to their images on the focal plane are presented. >

http://ieeexplore.ieee.org/iel2/815/3148/00100651.pdf

Robot vision

We propose, analyze, and test an alternating minimization algorithm for recovering images from blurry and noisy observations with total variation (TV) regularization. This algorithm arises from a new half-quadratic model applicable to not only the anisotropic but also the isotropic forms of TV discretizations. The per-iteration computational complexity of the algorithm is three fast Fourier transforms. We establish strong convergence properties for the algorithm including finite convergence for some variables and relatively fast exponential (or $q$-linear in optimization terminology) convergence for the others. Furthermore, we propose a continuation scheme to accelerate the practical convergence of the algorithm. Extensive numerical results show that our algorithm performs favorably in comparison to several state-of-the-art algorithms. In particular, it runs orders of magnitude faster than the lagged diffusivity algorithm for TV-based deblurring. Some extensions of our algorithm are also discussed.

/pdf/a-new-alternating-minimization-algorithm-for-total-variation-p0vrnncv59.pdf

A New Alternating Minimization Algorithm for Total Variation Image Reconstruction

We introduce a new iterative regularization procedure for inverse problems based on the use of Bregman distances, with particular focus on problems arising in image processing. We are motivated by the problem of restoring noisy and blurry images via variational methods by using total variation regularization. We obtain rigorous convergence results and effective stopping criteria for the general procedure. The numerical results for denoising appear to give significant improvement over standard models, and preliminary results for deblurring/denoising are very encouraging.

/pdf/an-iterative-regularization-method-for-total-variation-based-3dl3sp5cav.pdf

An Iterative Regularization Method for Total Variation-Based Image Restoration

We study a functional with variable exponent, $1\leq p(x)\leq 2$, which provides a model for image denoising, enhancement, and restoration. The diffusion resulting from the proposed model is a combination of total variation (TV)-based regularization and Gaussian smoothing. The existence, uniqueness, and long-time behavior of the proposed model are established. Experimental results illustrate the effectiveness of the model in image restoration.

Variable Exponent, Linear Growth Functionals in Image Restoration

As a powerful statistical image modeling technique, sparse representation has been successfully used in various image restoration applications. The success of sparse representation owes to the development of the l1-norm optimization techniques and the fact that natural images are intrinsically sparse in some domains. The image restoration quality largely depends on whether the employed sparse domain can represent well the underlying image. Considering that the contents can vary significantly across different images or different patches in a single image, we propose to learn various sets of bases from a precollected dataset of example image patches, and then, for a given patch to be processed, one set of bases are adaptively selected to characterize the local sparse domain. We further introduce two adaptive regularization terms into the sparse representation framework. First, a set of autoregressive (AR) models are learned from the dataset of example image patches. The best fitted AR models to a given patch are adaptively selected to regularize the image local structures. Second, the image nonlocal self-similarity is introduced as another regularization term. In addition, the sparsity regularization parameter is adaptively estimated for better image restoration performance. Extensive experiments on image deblurring and super-resolution validate that by using adaptive sparse domain selection and adaptive regularization, the proposed method achieves much better results than many state-of-the-art algorithms in terms of both PSNR and visual perception.

/pdf/image-deblurring-and-super-resolution-by-adaptive-sparse-2xqs03mycg.pdf

Image Deblurring and Super-Resolution by Adaptive Sparse Domain Selection and Adaptive Regularization

We introduce a new method for image smoothing based on a fourth-order PDE model. The method is tested on a broad range of real medical magnetic resonance images, both in space and time, as well as on nonmedical synthesized test images. Our algorithm demonstrates good noise suppression without destruction of important anatomical or functional detail, even at poor signal-to-noise ratio. We have also compared our method with related PDE models.

http://ee.sharif.edu/~miap/paper/88210583.pdf

Noise removal using fourth-order partial differential equation with applications to medical magnetic resonance images in space and time

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.

/pdf/a-binary-level-set-model-and-some-applications-to-mumford-2trhq3hfmf.pdf

A binary level set model and some applications to Mumford-Shah image segmentation

A noise removal technique using partial differential equations (PDEs) is proposed here. It combines the Total Variational (TV) filter with a fourth-order PDE filter. The combined technique is able to preserve edges and at the same time avoid the staircase effect in smooth regions. A weighting function is used in an iterative way to combine the solutions of the TV-filter and the fourth-order filter. Numerical experiments confirm that the new method is able to use less restrictive time step than the fourth-order filter. Numerical examples using images with objects consisting of edge, flat and intermediate regions illustrate advantages of the proposed model.

http://folk.uib.no/nmaxt/papers/linear.pdf

Iterative Image Restoration Combining Total Variation Minimization and a Second-Order Functional

Scale Space and Variational Methods in Computer Vision

In this paper we propose a variant of the level set formulation for identifying curves separating regions into different phases. In classical level set approaches, the sign of n level set functions are utilized to identify up to 2" phases. The novelty in our approach is to introduce a piecewise constant level set function and use each constant value to represent a unique phase. If 2" phases should be identified, the level set function must approach 2" predetermined constants. We just need one level set function to represent 2" unique phases, and this gains in storage capacity. Further, the reinitializing procedure requested in classical level set methods is superfluous using our approach. The minimization functional for our approach is locally convex and differentiable and thus avoids some of the problems with the nondifferentiability of the Delta and Heaviside functions. Numerical examples are given, and we also compare our method with related approaches.

/pdf/a-variant-of-the-level-set-method-and-applications-to-image-3h4o2ekeni.pdf

Marius Lysaker

Papers

Noise removal using fourth-order partial differential equation with applications to medical magnetic resonance images in space and time

A binary level set model and some applications to Mumford-Shah image segmentation

Iterative Image Restoration Combining Total Variation Minimization and a Second-Order Functional

Scale Space and Variational Methods in Computer Vision

A variant of the level set method and applications to image segmentation