Sharif Digital Repository

We have shown how to construct multiresolution structures for reversing subdivision rules using global least squares models (Samavati and Bartels, Computer Graphics Forum, 18(2):97-119, June 1999). As a result, semiorthogonal wavelet systems have also been generated. To construct a multiresolution surface of an arbitrary topology, however, biorthogonal wavelets are needed. In Bartels and Samavati (Journal of Computational and Applied Mathematics, 119:29-67, 2000) we introduced local least squares models for reversing subdivision rules to construct multiresolution curves and tensor product surfaces, noticing that the resulting wavelets were biorthogonal (under an induced inner product). Here,... 

Recognition and correction of inhomogeneous displacement caused by patient's movement has been recently discussed as an interesting topic in medical image processing. Considering consistency in general structure of the image during distortion, histogram could be employed as a fast implementation method in feature domain. Accordingly, attribute vectors could be defined for each pixel based on spatial features to find corresponding points in two images. Consequently a point-based and non-rigid transformation approach will be designed. A B-spline image registration has been applied to match those pairs with a defined smoothness factor. This algorithm is a step-by-step registration process... 

Site-specific ultrawideband propagation modeling involves dealing with frequency variations of the propagation mechanisms and antenna patterns in the ray tracing program. Typically, electromagnetic field calculations have to be performed in a lot of frequencies to accurately construct the frequency response of the channel at a receiving point. This imposes a heavy computational burden on ray tracing specially in calculating the coverage map or finding the statistics of channel parameters where the number of receiving locations is large. In this paper, the computational complexity of ray tracing in ultrawideband propagation modeling is reduced by using cubic B-spline interpolation. The... 

Ray tracing has been widely accepted as a versatile and reliable method for indoor propagation modeling. Several published articles have addressed the computational efficiency and reliability as the most challenging problems of ray tracing and have presented various solutions. Such challenges are discussed in this paper and some possible solutions are presented  

Based on the analogy between the B-spline curve modeling and the force-deflection behavior of a beam subjected to lateral point loads, an extension to the B-spline surface modeling method was introduced. The proposed method has strong extrapolating capability and can develop accurate surface models over an incomplete net of data points without affecting the original data. Extrapolation of the incomplete part of the data net Is conducted simultaneously with interpolation of the existing part, with no need to recalculation. Approximation or data smoothing is a natural extension of the method, however, the smoothing intensity can be controlled continuously without reducing the number of spline... 

The registration of images is a fundamental task in numerous applications in medical image processing. In this paper, a novel registration technique is proposed which combines landmark and intensity based approaches. In this framework, the free form deformation (FFD) is used as transformation which is the key point of our algorithm. Landmarks with FFD transformation define the guidance surface which increases robustness of intensity based registration to bias field (bias noise). In fact, the performance of registration is improved by matching both landmark and intensity information. The experimental results show that the proposed method is more accurate than only intensity based method... 

In site-specific ultrawideband propagation modelling, electromagnetic field calculations need to be performed by ray tracing at numerous frequencies of the band in order to properly include the frequency variations of the propagation mechanisms and antenna patterns. This is computationally intensive especially in calculating the coverage map or finding the statistics of the channel parameters where field calculations need to be carried out at a lot of receiver locations. In this study, the cubic B-spline function is incorporated in ray tracing to increase the computational efficiency of site-specific ultrawideband propagation modelling. This function can accurately reconstruct a signal from... 

Based on the force-deflection equation for a beam subjected to lateral point loads, a C2 continuous piecewise bicubic mathematical representation was proposed to model complicated geometrical surfaces, e.g. the articular surfaces of human joints. The method was then extended so that it could be used for mathematical modelling of incomplete nets of data points, as well as smoothing of noisy and/or filtering of erroneous data points. Mathematical techniques were also developed to calculate the required unknown parameters explicitly, with no need to solve the system of equations simultaneously. The performance of the proposed method was evaluated on a number of surface modelling problems,... 

Rapidly exploring random trees (RRT) are sampling-based approaches being widely applied for path planning of mobile robots. Since the output of these algorithms usually is a stream of discrete lines involving discontinuity at the linking points, kinematic constraints restrict the robot's movements. Consequently, robots may not pass discrete points in the path correctly. Hence, the using CAGD (Computer-Aided Geometry Design) curves can run simultaneously alongside those algorithms or may run after that to make a smooth path and that's the way in which non-holonomic constraints can be considered perfect and robots can be droved autonomously across them about the collision detection method... 

This paper presents an offline path planning method in 3D space for a surveillance aerial vehicle. In this method, the aerial vehicle is supposed to visit particular points on the path, and the collision between the vehicle and the fixed obstacles in the environment must be avoided. In order to accomplish the mission, first, the path is generated using B-splines. Then, the feasibility of tracking the designed path for the vehicle is considered by analyzing the vehicle's dynamic constraints, such as limitations on deflections of control surfaces. The analysis is supported by a simulation. Potential extension of the proposed analysis to multiple aerial vehicles has been also discussed at the... 

In this paper, we propose a frequency-independent method for calculation of scattered electromagnetic (EM) fields by the human body in millimeter-wave (MMW) band. The surface of the body is accurately modeled by non-uniform rational B-spline (NURBS) surfaces and is illuminated by a plane wave. The scattered EM fields are formulated by physical optics (PO) approximation. This approximation yields PO surface highly oscillatory integrals that are solved by numerical steepest descent path (NSDP) method, frequency-independently. This paper provides an efficient and accurate method for considering human body in indoor propagation, surveillance and medical imaging, and detection of human body by... 

This paper is devoted to the characterization of an extended family of continuous-time autoregressive moving average (CARMA) processes that are solutions of stochastic differential equations driven by white Lévy innovations. These are completely specified by: 1) a set of poles and zeros that fixes their correlation structure and 2) a canonical infinitely divisible probability distribution that controls their degree of sparsity (with the Gaussian model corresponding to the least sparse scenario). The generalized CARMA processes are either stationary or nonstationary, depending on the location of the poles in the complex plane. The most basic nonstationary representatives (with a single pole... 

In this paper we address the electromagnetic (EM) wave scattering from human body in millimeter-wave (MMW) band and 5G networks, where human body can be considered as an electrically large object. The complicated geometry of human body is accurately modeled using non-uniform rational B-spline (NURBS) surfaces as a thin dielectric slab with permittivity of human skin. Physical optics (PO) approximation is used to formulate the scattering problem. To solve highly oscillatory PO integrals, triangular boundary-rectangular mesh (TBRM) algorithm is exploited. This algorithm provides frequency-independent solution for PO integrals and allows frequency-independent meshing of the human body surface.... 

Needle insertion simulation and planning systems (SPSs) will play an important role in diminishing inappropriate insertions into soft tissues and resultant complications. Difficulties in SPS development are due in large part to the computational requirements of the extensive calculations in finite element (FE) models of tissue. For clinical feasibility, the computational speed of SPSs must be improved. At the same time, a realistic model of tissue properties that reflects large and velocity-dependent deformations must be employed. The purpose of this study is to address the aforementioned difficulties by presenting a cost-effective SPS platform for needle insertions into the liver. The study...