An efficient method for visual data compression is presented which combines generalized Peano (1890) scan and a lapped orthogonal transform (LOT) The Peano scan, an application of the Peano curve to the scanning of images, is used locally to cluster highly correlated pixels The new set of data is compressed using a LOT The LOT is a tool for block transform coding with basis functions that overlap adjacent blocks The blocking effect is reduced significantly by applying LOT An adaptive procedure is developed to encode image blocks at low bit rates without any visible blocking effects The compression method was tested on several images >

Image data ordering and compression using Peano scan and LOT

Hilbert curve is one of the space-filling curves published by Peano. There are several applications using this curve such as image processing, computer hologram, etc. In this paper, we concentrate on a lossy compression technique for a gray image using the Hilbert curve. The merit of this curve is to pass through all points in a quadrant, and it always moves to the neighbor quadrant. Our method is based on this neighborhood property, by a simple segmentation of the scanned one-dimensional data using a zero order interpolation. From our experiments, we have confirmed that in spite of the simple computation in comparison to JPEG, acceptable quality images can be obtained at bit-rates above 0.6 bit/pixel.

A gray image compression using a Hilbert scan

This letter presents a novel application of Peano scanning (PS) to expedite the partial distance search (PDS) when coding image blocks using vector quantization (VQ). It computes and stores a set of sorted tables of PS values of selected feature vectors associated with the codevectors. A PS acts as a transform from a higher dimension to a single dimension while preserving neighborhood adjacency. Coding of an input block is accomplished by finding the closest PS value to that of the input and its corresponding table. PDS proceeds from the codevector of this PS value. Computational complexity is greatly reduced with the PS value easily obtained in hardware and real time. >

Peano scanning partial distance search for vector quantization

The Hilbert curve is one of the space-filling curves published by G. Peano. There are several applications using this curve such as image processing, computer graphics, etc. We concentrate on a compression technique for color images using the Hilbert curve. The merit of this curve is to pass through all points in a quadrant, and always to move to the neighboring quadrant. Our method is based on this neighborhood property by a simple segmentation of the scanned one dimensional data using a zero order interpolation. From our experiments, we have confirmed that inspite of the simple computation in comparison to JPEG, acceptable quality images can be obtained at the same bit-rates.

Color image compression using a Hilbert scan

Fast methods for split codebooks

The main problem for vector quantisation is the codebook generation. The LBG method solves it with an iterative approach. This algorithm needs a long training sequence and an initial approximation of the codebook. These problems may be overcome by using space filling curves, also called Peano's curves, which are mappings from the unitary interval (image point) to the unitary hypercube. By using this kind of mapping the generation of the codebook, is reduced to the computation of the one-dimensional (optimum) quantiser associated to the probability density function (pdf) of the image points on the Hilbert curve. The paper describes the way of applying these mappings: a new algorithm is derived, generating codebooks for vector quantisation, and experimental results on image coding are provided.

M. Guglielmo

Papers

A technique using a one-dimensional mapping for vector quantisation of images

e Laboratori Telecomunicazion i S.p.A.