Cartoon-Residual Image Decompositions with Application in Fingerprint Recognition

by Robin Richter
Doctoral thesis
Date of Examination:2019-11-06
Date of issue:2019-12-11
Advisor:Prof. Dr. Stephan Huckemann
Referee:Prof. Dr. Stephan Huckemann
Referee:Prof. Dr. Gerlind Plonka-Hoch
Persistent Address: http://dx.doi.org/10.53846/goediss-7762

 

 

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Abstract

English

Image decompositions into a piecewise smooth part - called a cartoon - and a residual part containing oscillating patterns and/or noise, proved to be very useful in automated image processing, for example in applications such as segmentation and classification, denoising and deblurring, or shape- and edge-detection. A major challenge poses the selection of an appropriate decomposition model for a specific application at hand. To tackle this problem, this thesis proposes a generalized cartoon-residual decomposition algorithm that features a high-dimensional set of continuous parameters. The goal is to obtain a highly flexible algorithm such that choosing a decomposition model can be reformulated as a parameter selection problem. The proposed generalization contains multiple well known models such as the Rudin-Osher-Fatemi model as special cases, whilst also including a range of novel cartoon-residual decompositions. This thesis provides existence, convergence and uniqueness results for fixed points of the generalized algorithm for varying subfamilies of parameters, respectively, laying a foundation for possible tuning or training. Furthermore, as a proof of concept, first experimental results for denosing and texture-removal are presented, illustrating potential benefits of the novel decompositions. As an application, a new fingerprint quality estimator based on an existing cartoon-texture-residual decomposition by Thai and Gottschlich is proposed.
Keywords: mathematical imaging; continuous optimization; fingerprint analysis; image decompositions; alternating direction method of multipliers; total variation in imaging
 
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