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| Author(s): |
Ricardo Dutra da Silva
Total Authors: 1
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| Document type: | Doctoral Thesis |
| Press: | Campinas, SP. |
| Institution: | Universidade Estadual de Campinas (UNICAMP). Instituto de Computação |
| Defense date: | 2013-05-11 |
| Examining board members: |
Hélio Pedrini;
João Paulo Papa;
Helton Hideraldo Bíscaro;
Jorge Stolfi;
Neucimar Jerônimo Leite
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| Advisor: | Hélio Pedrini |
| Abstract | |
The Morse theory is important for studying the topology of scalar functions such as elevation of terrains and data from physical simulations, which relates the topology of a function to critical points. The smooth theory has been adapted to discrete data through constructions such as the Morse-Smale complexes and the discrete Morse complex. Morse complexes have been applied to image processing, however, there are still challenges involving algorithms and practical considerations for computation and modeling of the complexes. Morse complexes can be used as means of defining the connectedness of interest points in images. Usually, interest points are considered as independent elements described by local information. Such an approach has its limitations since local information may not suffice for describing certain image regions. Minimum and maximum points are widely used as interest points in images, which can be obtained from Morse complexes, as well as their connectivity in the image space. This thesis presents an algorithmic and data structure driven approach to computing the discrete Morse complex of 2-dimensional images. The construction is optimal and allows easy manipulation of the complex. Theoretical and applied results are presented to show the effectiveness of the method. Applied experiments include the computation of persistent homology and hierarchies of complexes over elevation terrain data. Another contribution is the proposition of a topological operator, called Local Morse Context (LMC), computed over Morse complexes, for extracting neighborhoods of interest points to explore the structural information in images. The LMC is used in the development of a matching algorithm, which helps reducing the number of incorrect matches between images and obtaining a confidence measure of whether a correspondence is correct or incorrect. The approach is tested in synthetic and challenging underwater stereo pairs of images, for which available methods may obtain many incorrect correspondences (AU) | |
| FAPESP's process: | 09/10627-5 - Video Segmentation Based On Descriptors Extracted from Wavelet Transforms |
| Grantee: | Ricardo Dutra da Silva |
| Support Opportunities: | Scholarships in Brazil - Doctorate |