The dissertation proposes a set of pyramidal compression algorithms over a loose wavelet basis, designed to minimize the entropy of the image representation. We discuss design principles and trade-offs.
The dissertation also proposes a non-uniform wavelet compression, which lets the user control the amount of distortion and compression in particular, arbitrarily specified, parts of the image: bringing some parts of the image into a sharp focus while progressively blurring the rest.
We develop a regularized discrete derivative of an image, which effectively removes the local background and fine-scale noise. Therefore, it may be used for localizing image patterns regardless of the lighting conditions, etc.
A discovery of the property of self-similarity of the pyramidal image transform has opened up an entirely new approach to compression: zooming out from a (possibly shrunken) low-resolution image producing a sharp and crisp ``natural looking'' high-resolution view. Thin lines remain thin upon expansion, translational invariance in maintained, and gradient fill is perfectly reproduced at any scale.
The multiresolutional transform algorithms and smart image magnification developed for still images are generalized to deal with moving pictures as a three-dimensional, spatio-temporal frame sequence, which permits rapid compression, and has potential for use in video transmission in real time.
Pyramidal Image Decompositions: A New Look
A poster presented at Data Compression Conference, Snowbird, Utah, 1993
Self-similarity of the Multiresolutional Image/Video
Decomposition: Smart Expansion as Compression of Still and Moving
Data Compression Conference, Snowbird, Utah, 1994
Compression with Iterated Function Systems, Finite Automata and Zerotrees: an elaboration of the relationship between Culik's algorithm, fractal compression and zero-tree encoding
The paper offers a plain-term interpretation of Culik’s image compression, a very capable yet undeservingly underrepresented method giving spectacular results. We explain Culik’s technique in image processing rather than formal automata terms. We demonstrate how closely it relates to Iterated Function System (IFS) fractal image compression: an IFS can be exactly transformed into Culik’s image code. Using this transformation, we prove that in a self-similar (part of an) image any zero wavelet coefficient is the root of a zerotree, or its branch.
The paper discusses the zerotree coding of (wavelet/projection) coefficients as a common predictor/corrector, applied vertically through different layers of a multiresolutional decomposition, rather than within the same view. This interpretation leads to an insight into the evolution of image compression techniques: from a causal single-layer prediction, to non-causal same-view predictions (wavelet decomposition among others) and to a causal cross-layer prediction (zerotrees, Culik’s method). A non-causal cross-level prediction appears to be the next step. Will someone take it?
Notes on Data Compression Conference '96, with detailed explanations of Culik's algorithm.
A better half of the notes is devoted to a remarkable and stunning method of compressing images using Finite Automata, which was invented/discovered by Dr. Karel Culik. The notes are the result of pondering over Culik's presentation and paper. Along the way, I noticed and corrected a few typos in his paper. I really took a stab at "reverse-engineering" of the compression and decompression algorithms, showing how they work step-by-step, to the point of showing pseudo-code and tracing through it.
Dr. Culik's website shows examples of WFA (Weighted Finite Automata) compression and contains his bibliography.
The presentation at the NASA workshop: a collection of web pages. I indeed presented the paper in a browser (Netscape). It was 1995; the Web was new.