arXiv subjects

Vikas Gupta

Publications and source records attributed to Vikas Gupta.

7 recordsLinked to original sources

arXiv2025

Uniform norm error estimate for rectangular finite element approximation of a 2D turning point problem

This work presents error analysis for a finite element method applied to a two-dimensional singularly perturbed convection-diffusion turning point problem. Utilizing a layer-adapted Shishkin mesh, we prove uniform convergence in the maximum norm in the x-layer regions and $\varepsilon$-independent bounds for the coarse region. The analysis, critically based on the properties of a discrete Green's function, guarantees the method's robustness and accuracy in capturing sharp solution layers.

math.NA↗

arXiv2020

Back to the Future: Joint Aware Temporal Deep Learning 3D Human Pose Estimation

We propose a new deep learning network that introduces a deeper CNN channel filter and constraints as losses to reduce joint position and motion errors for 3D video human body pose estimation. Our model outperforms the previous best result from the literature based on mean per-joint position error, velocity error, and acceleration errors on the Human 3.6M benchmark corresponding to a new state-of-the-art mean error reduction in all protocols and motion metrics. Mean per joint error is reduced by 1%, velocity error by 7% and acceleration by 13% compared to the best results from the literature. Our contribution increasing positional accuracy and motion smoothness in video can be integrated with future end to end networks without increasing network complexity. Our model and code are available at https://vnmr.github.io/ Keywords: 3D, human, image, pose, action, detection, object, video, visual, supervised, joint, kinematic

cs.CV↗

arXiv2019

Parameter-uniform fitted mesh higher order finite difference scheme for singularly perturbed problem with an interior turning point

In this paper, a parameter-uniform fitted mesh finite difference scheme is constructed and analyzed for a class of singularly perturbed interior turning point problems. The solution of this class of turning point problem possess two outflow exponential boundary layers. Parameter-explicit theoretical bounds on the derivatives of the analytical solution are given, which are used in the error analysis of the proposed scheme. The problem is discretized by a hybrid finite difference scheme comprises of midpoint-upwind and central difference operator on an appropriate piecewise-uniform fitted mesh. An error analysis has been carried out for the proposed scheme by splitting the solution into regular and singular components and the method has been shown second order uniform convergent except for a logarithmic factor with respect to the singular perturbation parameter. Some relevant numerical examples are also illustrated to verify computationally the theoretical aspects. Numerical experiments show that the proposed method gives competitive results in comparison to those of other methods exist in the literature.

math.NA↗

arXiv2019

Uncalibrated Deflectometry with a Mobile Device on Extended Specular Surfaces

We introduce a system and methods for the three-dimensional measurement of extended specular surfaces with high surface normal variations. Our system consists only of a mobile hand held device and exploits screen and front camera for Deflectometry-based surface measurements. We demonstrate high quality measurements without the need for an offline calibration procedure. In addition, we develop a multi-view technique to compensate for the small screen of a mobile device so that large surfaces can be densely reconstructed in their entirety. This work is a first step towards developing a self-calibrating Deflectometry procedure capable of taking 3D surface measurements of specular objects in the wild and accessible to users with little to no technical imaging experience.

cs.CV↗

arXiv2017

Automatic Trimap Generation for Image Matting

Image matting is a longstanding problem in computational photography. Although, it has been studied for more than two decades, yet there is a challenge of developing an automatic matting algorithm which does not require any human efforts. Most of the state-of-the-art matting algorithms require human intervention in the form of trimap or scribbles to generate the alpha matte form the input image. In this paper, we present a simple and efficient approach to automatically generate the trimap from the input image and make the whole matting process free from human-in-the-loop. We use learning based matting method to generate the matte from the automatically generated trimap. Experimental results demonstrate that our method produces good quality trimap which results into accurate matte estimation. We validate our results by replacing the automatically generated trimap by manually created trimap while using the same image matting algorithm.

cs.CV↗

arXiv2015

Local principle satisfying high order total variation diminishing approximation for non-sonic data extrema

The main contribution of this work is to construct higher than second order accurate total variation diminishing (TVD) schemes which can preserve high accuracy at non-sonic extrema with out induced local oscillations. It is done in the framework of local maximum principle (LMP) and non-conservative formulation. The representative uniformly second order accurate schemes are converted in to their non-conservative form using the ratio of consecutive gradient. These resulting schemes are analyzed for their non-linear LMP/TVD stability bounds using the local maximum principle. Based on the bounds, second order accurate hybrid numerical schemes are constructed using a shock detector. Numerical results are presented to show that such hybrid schemes yield TVD approximation with second or higher order convergence rate for smooth solution with extrema.

math.NA↗

arXiv2010

Computer Aided Design Modeling for Heterogeneous Objects

Heterogeneous object design is an active research area in recent years. The conventional CAD modeling approaches only provide geometry and topology of the object, but do not contain any information with regard to the materials of the object and so can not be used for the fabrication of heterogeneous objects (HO) through rapid prototyping. Current research focuses on computer-aided design issues in heterogeneous object design. A new CAD modeling approach is proposed to integrate the material information into geometric regions thus model the material distributions in the heterogeneous object. The gradient references are used to represent the complex geometry heterogeneous objects which have simultaneous geometry intricacies and accurate material distributions. The gradient references helps in flexible manipulability and control to heterogeneous objects, which guarantees the local control over gradient regions of developed heterogeneous objects. A systematic approach on data flow, processing, computer visualization, and slicing of heterogeneous objects for rapid prototyping is also presented.

cs.CE↗