In general, mesh smoothing is performed by minimizing the discrete energy function for the surface. One of the major problems in mesh smoothing is to prevent the mesh from shrinking. In this paper, we propose a novel volume constraint to address the shrinking problem in mesh smoothing. Our key observation is that the mesh can be efficiently smoothed patch by patch in a signal processing manner,...

In this work, we identify the power-optimal wire spacing as a geometric program. Its solution is a vector of individual distances between the wires. To quantify the optimization potential by this method we model the output of a grid based router with a set of parallel wires. A comparison of the power values before and after geometric optimization shows that the optimization potential lies well ...

In this paper, we propose a unified framework to address the problem of cytological computeraided diagnosis. Such an approach relies on our previously introduced formalisms: general formulation of discrete functional regularization, PDEs based morphology and geometric diffusion on graphs. The approach is illustrated through two applications in cytopathology, with examples of nucleus extraction ...

Topography affects the fraction of scene components canopy and background, resulting in observed reflectance distortion. Modeling over rugged terrain needs to account for topographic effects. For this purpose, existing models greatly increased mathematical complexity while improving description crown structure, which dramatically decreased computational efficiency so as limit their universal ap...

The quest for the discovery of mathematical principles that underlie biological phenomena is ancient and ongoing. We present a geometric analysis of the complex interdigitated pavement cells in the Arabidopsis thaliana (Col.) adaxial epidermis with a view to discovering some geometric characteristics that may govern the formation of this tissue. More than 2,400 pavement cells from 10, 17 and 24...

The sizes of living organisms range over twenty orders magnitude. Within the same species, size individuals also varies according to environmental conditions which they are subjected. From studies conducted on as diverse drosophila, salamander or mouse, laws and conserved mechanisms emerge that shed light fundamental aspects growth, but more medical issues such tissue regeneration, metabolic ho...

The classification of geometric decorative motifs has tended to emphasise the geometric by comparing the decoration to mathematically perfect constructions. Focussing on spirals as exemplars, this paper proposes that additional information may be gleaned from historic decoration on the assumption that such decoration often does not conform exactly to mathematically correct constructions. Shape-...

Study on properties of Sierpinski-type fractals, including dimension, measure, Lipschitz equivalence, etc is very interesting. It is well know that studying fractal theory relies on in-depth observation and analysis to topological structures of fractals and their geometric constructions. But most works of simulating fractals are for graphical goal and often done by non-mathematical researchers....