The smoothness property of refinable functions is an important issue in all multiresolution analysis and has a strong impact on applications of wavelets to image processing, geometric and numerical solutions of elliptic partial differential equations. The purpose of this paper is to characterize the smoothness properties of refinable functions with exponentially decaying masks and an isotropic ...

Multidimensional curve fitting has applications in signal and image processing, control, and other engineering disciplines. The two important data fitting criteria are accuracy of the fit and the smoothness of the fit. In this paper, we discuss an algorithm for multidimensional smooth curve fitting where the cost function is a combination of two terms, one dealing with accuracy and the other on...

We propose a unified framework for boundary finding, where a Bayesian formulation, based on prior knowledge and the edge information of the input image (likelihood), is employed. The prior knowledge in our framework is based on principal component analysis of four different covariance matrices corresponding to independence, smoothness, statistical shape and combined models, respectively. Indeed...

We consider the smoothness of solutions of a system of refinement equations written in the form φ = ∑ α∈Z a(α)φ(2 · − α), where the vector of functions φ = (φ1, . . . , φr) is in (Lp(R)) and a is a finitely supported sequence of r× r matrices called the refinement mask. We use the generalized Lipschitz space Lip∗(ν, Lp(R)), ν > 0, to measure smoothness of a given function. Our method is to rela...

Magnetic resonance images are affected by motion artefacts due to breathing and cardiac beating that occur during the acquisition. Methods for joint reconstruction of image and motion have been proposed recently. Such optimization problems are ill-conditioned, therefore regularization methods are required such as motion smoothness constraints using the Tikhonov method. However with Tikhonov met...

We present a new image completion method based on an additional large displacement view (LDV) of the same scene for faithfully repairing large missing regions on the target image in an automatic way. A coarse-to-fine distortion correction algorithm is proposed to minimize the perspective distortion in the corresponding parts for the common scene regions on the LDV image. First, under the assump...

Here we study the extreme visual recovery problem, in which over 90% of pixel values in a given image are missing. Existing low rank-based algorithms are only effective for recovering data with at most 90% missing values. Thus, we exploit visual data’s smoothness property to help solve this challenging extreme visual recovery problem. Based on the Discrete Cosine Transformation (DCT), we propos...

Nowadays color image processing is an essential issue in computer vision. Variational formulations provide a framework for color image restoration, smoothing and segmentation problems. The solutions of variational models can be obtained by minimizing appropriate energy functions and this minimization is usually performed by continuous partial differential equations (PDEs). The problem is usuall...

We consider the smoothness of solutions of a system of reenement equations written in the form as = X 2ZZ a()(2 ?) where the vector of functions = (1 ; : : : ; r) T is in (L p (IR)) r and a is a nitely supported sequence of r r matrices called the reenement mask. We use the generalized Lipschitz space Lip (; L p (IR)), > 0, to measure smoothness of a given function. Our method is to relate the ...

A general variational framework for image approximation and segmentation is introduced. By using a continuous “line-process” to represent edge boundaries, it is possible to formulate a variational theory of image segmentation and approximation in which the boundary function has a simple explicit form in terms of the approximation function. At the same time, this variational framework is general...