Projects per year
Abstract
This thesis presents work in the direction of generating smooth surfaces from
linear cross sections embedded in R2 and R3 using homotopy continuation. The
methods developed in this research are generic and can be applied to higher
dimensions as well. Two types of problems addressed in this research are reconstruction
from an organised set of linear cross sections and reconstruction from
an arbitrary set of linear cross sections. The first problem is looked upon in the
context of acoustic signals wherein the cross sections show a definite geometric
arrangement. A reconstruction in this case can take advantage of the inherent
arrangement. The problem of reconstruction from arbitrary cross sections is
a generic problem and is also shown to be solved here using the mathematical
tool of continuous deformations. As part of a complete processing, segmentation
using level set methods is explored for acoustic images and fast GPU (Graphics
Processing Unit) based methods are suggested for a streaming computation on
large volumes of data.
Validation of results for acoustic images is not straightforward due to unavailability
of ground truth. Accuracy figures for the suggested methods are provided
using phantom object with known geometry. The results of the methods shown
here can be used to gain objective knowledge about the reconstructed features.
It is envisioned that due to the generic nature of the algorithms developed in
this research, domains other than fisheries research can benefit from the reconstruction
algorithms.
Original language  English 

Place of Publication  Kgs. Lyngby, Denmark 

Publisher  Technical University of Denmark 
Publication status  Published  Sep 2010 
Series  IMMPHD2010234 

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Projects
 1 Finished

Homotopy based 3D reconstruction of water columns from 2D cross section acoustic data
Sharma, O., Hansen, V. L., Sellarès, J. A., Antón Castro, F. & Christensen, N. J.
15/07/2007 → 29/09/2010
Project: PhD