Search results for "Computer Science::Graphics"
showing 10 items of 67 documents
Spline histogram method for reconstruction of probability density function of clusters of galaxies
2003
We describe the spline histogram algorithm which is useful for visualization of the probability density function setting up a statistical hypothesis for a test. The spline histogram is constructed from discrete data measurements using tensioned cubic spline interpolation of the cumulative distribution function which is then differentiated and smoothed using the Savitzky-Golay filter. The optimal width of the filter is determined by minimization of the Integrated Square Error function. The current distribution of the TCSplin algorithm written in f77 with IDL and Gnuplot visualization scripts is available from http://www.virac.lv/en/soft.html
The geometry of surfaces in 4-space from a contact viewpoint
1995
We study the geometry of the surfaces embedded in ℝ4 through their generic contacts with hyperplanes. The inflection points on them are shown to be the umbilic points of their families of height functions. As a consequence we prove that any generic convexly embedded 2-sphere in ℝ4 has inflection points.
Entropy dissipation of moving mesh adaptation
2012
Non-uniform grids and mesh adaptation have been a growing part of numerical simulation over the past years. It has been experimentally noted that mesh adaptation leads not only to locally improved solution but also to numerical stability of the underlying method. There have been though only few results on the mathematical analysis of these schemes due to the lack of proper tools that incorporate both the time evolution and the mesh adaptation step of the overall algorithm. In this paper we provide a method to perform the analysis of the mesh adaptation method, including both the mesh reconstruction and evolution of the solution. We moreover employ this method to extract sufficient condition…
The Local Fractional Derivative of Fractal Curves
2008
Fractal curves described by iterated function system (IFS) are generally non-integer derivative. For that we use fractional derivative to investigate differentiability of this curves. We propose a method to calculate local fractional derivative of a curve from IFS property. Also we give some examples of IFS representing the slopes of the right and left half-tangent of the fractal curves.
Spectral clustering to model deformations for fast multimodal prostate registration
2012
International audience; This paper proposes a method to learn deformation parameters off-line for fast multimodal registration of ultrasound and magnetic resonance prostate images during ultrasound guided needle biopsy. The method is based on a learning phase where deformation models are built from the deformation parameters of a splinebased non-linear diffeomorphism between training ultrasound and magnetic resonance prostate images using spectral clustering. Deformation models comprising of the eigen-modes of each cluster in a Gaussian space are applied on a test magnetic resonance image to register with the test ultrasound prostate image. The deformation model with the least registration …
Representation of NURBS surfaces by Controlled Iterated Functions System automata
2019
Iterated Function Systems (IFS) are a standard tool to generate fractal shapes. In a more general way, they can represent most of standard surfaces like Bézier or B-Spline surfaces known as self-similar surfaces. Controlled Iterated Function Systems (CIFS) are an extension of IFS based on automata. CIFS are basically multi-states IFS, they can handle all IFS shapes but can also manage multi self-similar shapes. For example CIFS can describe subdivision surfaces around extraordinary vertices whereas IFS cannot. Having a common CIFS formalism facilitates the development of generic methods to manage interactions (junctions, differences...) between objects of different natures.This work focuses…
Efficient Implementation of Multiresolution Triangle Strips
2002
Triangle meshes are currently the most popular standard modelto represent polygonal surfaces. Drawing these meshes as a set of independent triangles involves sending a vast amount of information to the graphic engine. It has been shown that using drawing primitives, such as triangle fans or strips, dramatically reduces the amount of information. Multiresolution Triangle Strips (MTS) uses the connectivity information to represent a mesh as a set of multiresolution triangles strips. These strips are the basis of both the storage and rendering stages. They allow the efficient management of a wide range of levels of detail. In this paper, we have taken advantage of the coherence property betwee…
Optical calibration of a multispectral imaging system based on interference filters
2005
We present a new approach to optically calibrate a multispectral imaging system based on interference filters. Such a system typically suffers from some blurring of its channel images. Because the effectiveness of spectrum reconstruction depends heavily on the quality of the acquired channel images, and because this blurring negatively affects them, a method for deblurring and denoising them is required. The blur is modeled as a uniform intensity distribution within a circular disk. It allows us to characterize, quantitatively, the degradation for each channel image. In terms of global reduction of the blur, it consists of the choice of the best channel for the focus adjustment according to…
Texture advection on discontinuous flows
2015
Texture advection techniques, which transport textures using a velocity field, are used to visualize the dynamics of a flow on a triangle mesh. Some flow phenomena lead to velocity fields with discontinuities that cause the deformation of the texture which is not properly controlled by these techniques. We propose a method to detect and visualize discontinuities on a flow, keeping consistent texture advection at both sides of the discontinuity. The method handles the possibility that the discontinuity travels across the domain of the flow with arbitrary velocity, estimating its speed with least-squares approximation. The technique is tested with different sample scenarios and with two avala…
Periodic Discrete Splines
2014
Periodic discrete splines with different periods and spans were introduced in Sect. 3.4. In this chapter, we discuss families of periodic discrete splines, whose periods and spans are powers of 2. As in the polynomial splines case, the Zak transform is extensively employed. It results in the Discrete Spline Harmonic Analysis (DSHA). Utilization of the Fast Fourier transform (FFT) enables us to implement all the computations in a fast explicit way.