A new approximation of the Mumford-Shah model is proposed for edge detection, which could handle open-ended curves and closed curves as well. The essential idea is to treat the curves by narrow regions, and use a sharp interface technique to solve the approximate Mumford-Shah model. A fast algorithm based on the augmented Lagrangian method is developed. Numerical results show that the proposed ...

We focus on the multi-class segmentation problem using the piecewise constant Mumford-Shah model in a graph setting. After formulating a graph version of the Mumford-Shah energy, we propose an efficient algorithm called the MBO scheme using threshold dynamics. Theoretical analysis is developed and a Lyapunov functional is proven to decrease as the algorithm proceeds. Furthermore, to reduce the ...

This paper proposes the implementation of the Mumford and Shah functional without using complex operations as multiplications and divisions. Our goal is to show that the achieved results in terms of performance/complexity trade-off are well suited for video applications of the Mumford and Shah functional, such as motion estimation based on segmentation techniques. To this purpose two implementa...

An explicit method for the construction of a tight wavelet frame generated by the Walsh polynomials with the help of extension principles was presented by Shah (Shah, 2013). In this article, we extend the notion of wavelet frames to periodic wavelet frames generated by the Walsh polynomials on R by using extension principles. We first show that under some mild conditions, the periodization of a...

The Mumford-Shah functional minimization, and related algorithms for image segmentation, involve a tradeoff between a twodimensional image structure and one-dimensional parametric curves (contours) that surround objects or distinct regions in the image. We propose an alternative functional that is independent of parameterization; it is a geometric functional which is given in terms of the geome...

this study is a description about the development of ceremonies and rituals and also the formation of religious system and the type of its opposition with the political system, after the official declaration of asna ashari (twelve imams) shiism in the safavid dynasty. the author believes that at least four development periods can be considered in iranian rituals in the safavid era. the first pe...

the bagratian clan was the oldest and the most legitimate in georgia and safavid was confident about them. during the reign of shah safi, the credit of bagrati clan was increased due to their valuable service to the monarch and fining his reign. in the beginning of the accession, he wanted set up the tent of her reign based on the new columb and overthrow old elements that was independent on sh...

Arsenic (As) contamination in drinking groundwater sources is a common environmental problem Pakistan. Therefore, we collected total of ( n = 81) samples from various sources, two districts’ namely Ghotki 44) and Nawab Shah 37) Sindh, Province, The current research aimed to investigate the hydrogeochemistry with elevated arsenic (As), its effect on health local population living study area, pot...

In this paper we introduce a notion of unilateral slope for the Mumford-Shah functional, and provide an explicit formula in the case of smooth cracks. We show that the slope is not lower semicontinuous and study the corresponding relaxed functional.

Let G → GL(n,C) be a representation of a complex reductive group. A theorem of Hilbert says that the algebra C[x1, . . . , xn] of invariant polynomials is finitely generated. Let Y be the projective variety defined by this graded algebra, and then we have a rational morphism π : C · · · → Y(C). A theorem on geometric reductivity of Mumford says that a point x ∈ C is regular for the map π if and...