M.Sc. Thesis: Image Compression by Using Weak Membrane Model

Yüksek Lisans Tezi: Yırtılabilir Zar Modeli  Yardımıyla Görüntü Sıkıştırma

Istanbul Technical University, Institute of Sciences and Technology, Aug. 1995

Abstract:

In this thesis, a regularized approach to image coding is presented. In this approach, both coding part and decoding part are based on the regularized solutions of the weak membrane modeling.
Boundary information of objects of an image, form a sparse data which is one of the most important representation of that image. Boundaries are the regions where sharp changes occur in pixel intensities. Regions except these discontinuities are smooth which means pixel values don't represent sharp changes. This property allows to determine the pixel values of smooth regions by using data along the two sides of edges which present at discontinuities. In a two dimensional image, the data corresponding the values of pixels neighboring to the edge locations produce a very sparse image. By using an appropriate surface reconstruction algorithm, a dense image similar to the original one can be reconstructed.
In both coding and decoding parts, weak membrane model which is a surface reconstruction algorithm, is used to eliminate noise, detect edges and  obtain the dense image from sparse edge information. Weak membrane model preserves discontinuities while smoothing the regions apart from boundaries. This model is expressed by a non-convex energy functional representing the behaviour of a membrane.
The method is applied to various synthetic and real images. The compression ratio for syntetic images is approximately 40:1 and for real images approximately 20:1.

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