Let G be a connected reductive linear algebraic group. We use geometric methods to investigate G-completely reducible subgroups of G, giving new criteria for G-complete reducibility. We show that a subgroup of G is G-completely reducible if and only if it is strongly reductive in G; this allows us to use ideas of R.W. Richardson and Hilbert– Mumford–Kempf from geometric invariant theory. We ded...

This work focuses on a parameter-free joint piecewise smooth image denoising and contour detection. Formulated as the minimization of discrete Mumford–Shah functional estimated via theoretically grounded alternating scheme, bottleneck such variational approach lies in need to fine-tune their hyperparameters, while not having access ground truth data. To that aim, Stein-like strategy providing o...

A climate dependent model is proposed to simulate the population of Aedes aegypti mosquito. In developing the model, average temperature of Shah Alam, Malaysia was used to determine the development rate of each stage of the life cycle of mosquito. Rainfall dependent function was proposed to simulate the hatching rate of the eggs under several assumptions. The proposed transition matrix was obta...

We want to understand he concentration of damage in microfractured elastic media. Due to the different scallings of the volume and area (or area and length in two dimensions) the traditional method of homogenization using periodic arrays of cells seems to fail when applied to the Mumford-Shah functional and to periodically fractured domains. In the present paper we are departing from traditiona...

Saleh Kambo, a court historian of Shah Jahan (1628-58), while discussing the buildings, frequently used the phrases such as “makan dilnasheen hai az nasheman hai nuzhat aafreen” which means “heart pleasing buildings and praiseworthy mansions”. Every Mughal building designed surpassed its predecessor in terms of its design quality and decorative details. From the selection of the site to final d...

We propose and analyze extensions of the Mumford-Shah functional for the color images. Our main motivation is the concept of images as surfaces. We also review most of the relevant theoretical background and computer vision literature.

We introduce several color image restoration algorithms based on the Mumford-Shah model and nonlocal image information. The standard Ambrosio-Tortorelli and Shah models are defined to work in a small local neighborhood, which are sufficient to denoise smooth regions with sharp boundaries. However, textures are not local in nature and require semi-local/non-local information to be denoised effic...

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...