Theses and Dissertations

Permanent URI for this collectionhttp://ir.daiict.ac.in/handle/123456789/1

Browse

Filters

2013 - 20202

Settings

Author: search.filters.author.Bansal, SumukhEnd date: 2023

Search Results

Now showing 1 - 2 of 2
  • Thumbnail Image
    ItemOpen Access
    3D shape deformations : a lie group based approach
    (Dhirubhai Ambani Institute of Information and Communication Technology, 2020) Bansal, Sumukh; Tatu, Aditya
    3D shapes are ubiquitous in many fundamental tasks of computer graphics and geometry processing. For many applications, new shapes have to be generated from the existing ones, for which it it imperative to understand and model shape of an object and its deformation. This thesis focuses on shape deformations and its applications. Real world 3D objects undergo complex, often non-rigid deformations. One way to model such deformations is using local affine transformations. It is thus important for applications like 3D animation, to understand the structure of affine transformations and come up with robust and efficient computational tools on the set of affine transformations. With such tools, applications like interactive shape deformation and mesh interpolation can be effectively dealt with. In this thesis, an interpolation framework for affine transformations, based on a Lie group representation of a tetrahedron is proposed. The proposed framework provides a intuitive closed form interpolation in all cases in contrast to existing approaches and preserves properties like isometry, reversibility, and monotonic change of volume. The proposed Lie group representation of the tetrahedron is extended to represent triangular and tetrahedral meshes. A detailed analysis of the invariance of the representation and interpolation to some choices made, is provided in the thesis. We demonstrate the applicability of the framework for several applications like interactive shape deformation, shape interpolation, morphing, and deformation transfer. The proposed interactive shape deformation algorithm is close to being real-time, while the mesh interpolation algorithm is able to handle nonregistered meshes and large deformation cases. The interactive shape deformavi tion algorithm is amenable to data-driven methods, and we hope to explore datadriven methods using our mesh representation in near future.
  • Thumbnail Image
    ItemOpen Access
    Manifold valued image segmentation
    (Dhirubhai Ambani Institute of Information and Communication Technology, 2013) Bansal, Sumukh; Tatu, Aditya
    Image segmentation is the process of partitioning a image into different regions or groups based on some characteristics like color, texture, motion or shape etc. Segmentation is an intermediate process for a large number of applications including object recognition and detection. Active contour is a popular variational model for object segmentation in images, in which the user initializes a contour which evolves in order to optimize an objective function designed such that the desired object boundary is the optimal solution. Recently, imaging modalities that produce Manifold valued images have come up, for example, DT-MRI images, vector fields. The traditional active contour model does not work on such images. In the work presented here we generalize the active contour model to work on Manifold valued images. Since usual gray-scale images are just an specific example of Manifold valued images, our method produce expected results on gray-scale images. As an application of proposed active contour model we we perform texture segmentation on gray-scale images by first creating an appropriate Manifold valued image. We demonstrate segmentation results for manifold valued images and texture images. Diversity of the texture segmentation problem Inspired us to propose a new active contour model for texture segmentation where we find the background/foreground texture regions in a given image by maximizing the geodesic distance between the interior and exterior covariance matrices. We also provide results using proposed method.