# Pattern Analysis Using Level Set Method.

## Date of Submission

December 2004

## Date of Award

Winter 12-12-2005

## Institute Name (Publisher)

Indian Statistical Institute

## Document Type

Master's Dissertation

## Degree Name

Master of Technology

## Subject Name

Computer Science

## Department

Electronics and Communication Sciences Unit (ECSU-Kolkata)

## Supervisor

Mukherjee, Dipti Prasad (ECSU-Kolkata; ISI)

## Abstract (Summary of the Work)

Patterns generated in nature often enchant us. Since reproducing the realism of the physical world is a major goal of computer graphics, patterns are important for rendering synthetic images and animations. However, patterns are so diverse that it is difficult to describe and generate them in a single framework. This motivates computer graphics people to propose different pattem generation models. Patterns are basically of two types periodic and quasi-periodic. Patterms, which occur in a regular manner or periodically, are called regular pattems. Spots of cheetah, coat pattem of zebra, spots of giraffe etc. are examples of periodic patterns. Pattems, which are repeated after long period or in other words, which occur in a quasi-periodie way, are called quasi-periodic patterns. An example of quasi-periodic pattern is human fingerprint.There are many patterm generation models in literature (1,3,4]. We address two models, which emulates patterns in physical world. Physical phenomena like compliance or stiffness' of a body, is optimized to create patterns in real world. This is also known as pattem generation through structural topology optimization. The term topology optimization' will be explained in the proper context. The underlying goal of this modei is to get the optimal material distribution of the structure, given certain forces and constraints applying on the structure. This is as if a goldsmith is giving different shapes to a piece of gold for creating different patterns. Other phenomenon of creation of pattems is biological phenomenon. These are based on some chemical reactions, which control pattern generation in biological world. For example the biological phenomena by which spots of cheetah, stripes of zebra, patterms of giraffe, spots of leopard etc are formed. The reaction-diffusion model proposed by Turing (1] was the pioneering work in this context. Among other models, Meinherdts stripe-formation model [3]. netlike structure generation model (3], models proposed by J.D. Murray [4] are well known.The motivation bahin proposed by J.D. Murray [4] are well known. The motivation behind our work is to study pattern generation models and to design a similar model using level set framework (8]. Level set is a curve evolution method. Here evolution of the curve is traced by embedding the curve into a higher dimensional surface. We generate patterns by evolving a curve under different conditions, motivated by physical and biological phenomena The main difference of our model with previous models is that level set based model of pattem generation is more efficient. Using level set method, the change is connectivity or topology of an evolving curve can be traced efficiently. This is important for pattern generation process. Reaction diffusion model of Turing is computationally expensive But the method what we have proposed faster than reaction-diffusion model.In Chapter 2, we discuss topology optimization model and reaction-diffusion model of pattern generation. In Chapter 3, curve evolution theory and level set model is described. In Chapter 4, we propose our model of pattern generation based on level set Stitlness of a mtrnal bodu framework. Also we apply our model of pattern generation to regenerate some oceluded patterms.In Chapter 5, we conclude by discussing about possible future work of the proposed approach In the next chapter we discuss how patterns are generated using shape optimization and reaction-diffusion approach.

## Control Number

ISI-DISS-2004-126

## Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

## DOI

http://dspace.isical.ac.in:8080/jspui/handle/10263/6296

## Recommended Citation

Chattopadhyay, Amit, "Pattern Analysis Using Level Set Method." (2005). *Master’s Dissertations*. 126.

https://digitalcommons.isical.ac.in/masters-dissertations/126

## Comments

ProQuest Collection ID: http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqm&rft_dat=xri:pqdiss:28843143