Multiphase Segmentation with Convex Relaxation of Phase Functions

An Approach to Combine Image Segmentation and Image Denoising

Leonie Knittelfelder (Autor)

Buch | Softcover

104 Seiten

2016
AV Akademikerverlag
9783330501669 (ISBN)

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This work presents a multiphase functional to segment and approximate a given gray scale image where the resulting image is smooth on the support of each phase function. Therefore, unique existence of the model functions is shown and then existence of a minimum of the functional with respect to functions in a convex relaxation of a set of characteristic functions is shown. This research puts a focus on image denoising and image segmentation simultaneously and uses both approaches in one functional. Moreover, since it is unsure if the functional is convex, a semi-gradient descent approach is established in a spatially continuous setting and later on in a finite dimensional setting. In order to prove certain features, a mollifying operator was introduced. Furthermore, a mapping that binds the update of the optimization process to have range in [0, 1] was used. The segmentation was performed with up to four characteristic functions, whereas segmentation with only two showed the best result. The work presented here has profound implications for future studies of a concurrent algorithm of image segmentation and denoising.

Leonie Knittelfelder, DI.: Master's degree programme in Industrial Mathematics at Graz University of Technology, Bachelor's degree programm in Mathematics at Karl Franzens University Graz.

Erscheinungsdatum	31.07.2016
Sprache	englisch
Maße	150 x 220 mm
Gewicht	171 g
Themenwelt	Mathematik / Informatik ► Mathematik
Schlagworte	Finite Element Method • image denoising • Image Processing • Image Segmentation • Phase Functions
ISBN-13	9783330501669 / 9783330501669
Zustand	Neuware