Scanning and Sequential Decision Making for Multi-Dimensional Data - Part I: the Noiseless Case

We investigate the problem of scanning and prediction ("scandiction", for short) of multidimensional data arrays. This problem arises in several aspects of image and video processing, such as predictive coding, for example, where an image is compressed by coding the error sequence resulting from scandicting it. Thus, it is natural to ask what is the optimal method to scan and predict a given image, what is the resulting minimum prediction loss, and whether there exist specific scandiction schemes which are universal in some sense. Specifically, we investigate the following problems: First, modeling the data array as a random field, we wish to examine whether there exists a scandiction scheme which is independent of the field's distribution, yet asymptotically achieves the same performance as if this distribution was known. This question is answered in the affirmative for the set of all spatially stationary random fields and under mild conditions on the loss function. We then discuss the scenario where a non-optimal scanning order is used, yet accompanied by an optimal predictor, and derive bounds on the excess loss compared to optimal scanning and prediction. This paper is the first part of a two-part paper on sequential decision making for multi-dimensional data. It deals with clean, noiseless data arrays. The second part deals with noisy data arrays, namely, with the case where the decision maker observes only a noisy version of the data, yet it is judged with respect to the original, clean data.Comment: 46 pages, 2 figures. Revised version: title changed, section 1 revised, section 3.1 added, a few minor/technical corrections mad

Mesh-based video coding for low bit-rate communications

In this paper, a new method for low bit-rate content-adaptive mesh-based video coding is proposed. Intra-frame coding of this method employs feature map extraction for node distribution at specific threshold levels to achieve higher density placement of initial nodes for regions that contain high frequency features and conversely sparse placement of initial nodes for smooth regions. Insignificant nodes are largely removed using a subsequent node elimination scheme. The Hilbert scan is then applied before quantization and entropy coding to reduce amount of transmitted information. For moving images, both node position and color parameters of only a subset of nodes may change from frame to frame. It is sufficient to transmit only these changed parameters. The proposed method is well-suited for video coding at very low bit rates, as processing results demonstrate that it provides good subjective and objective image quality at a lower number of required bits

Vector Quantization Video Encoder Using Hierarchical Cache Memory Scheme

A system compresses image blocks via successive hierarchical stages and motion encoders which employ caches updated by stack replacement algorithms. Initially, a background detector compares the present image block with a corresponding previously encoded image block and if similar, the background detector terminates the encoding procedure by setting a flag bit. Otherwise, the image block is decomposed into smaller present image subblocks. The smaller present image subblocks are each compared with a corresponding previously encoded image subblock of comparable size within the present image block. When a present image subblock is similar to a corresponding previously encoded image subblock, then the procedure is terminated by setting a flag bit. Alternatively, the present image subblock is forwarded to a motion encoder where it is compared with displaced image subblocks, which are formed by displacing previously encoded image subblocks by motion vectors that are stored in a cache, to derive a first distortion vector. When the first distortion vector is below a first threshold TM, the procedure is terminated and the present image subblock is encoded by setting flag bit and a cache index corresponding to the first distortion vector. Alternatively, the present image subblock is passed to a block matching encoder where it is compared with other previously encoded image subblocks to derive a second distortion vector. When the second distortion vector is below a second threshold Tm, the procedure is terminated by setting a flag bit, by generating the second distortion vector, and by updating the cache.Georgia Tech Research Corporatio

Tchebichef Moment Based Hilbert Scan for Image Compression

Image compression is now essential for applications such as transmission and storage in data base, so we need to compress a vast amount of information whereas, the compressed ratio and quality of compressed image must be enhanced, for this reason, this paper develop a new algorithm that used a discrete orthogonal Tchebichef moment based Hilbert curve for image compression. The analyzed image was divided into 8×8 image sub-blocks, the Tchebichef moment has been applied to each one, and then the transformed coefficients 8×8 sub-block shall be reordered in Hilbert scan into a linear array, at this step Huffman coding is implemented. Experimental results show that this algorithm improves the coding efficiency on the one hand; and on the other hand the quality of reconstructed image is also not significantly decreased. Keywords: Huffman Coding, Tchebichef Moment Transforms, Orthogonal Moment Functions, Hilbert, zigzag scan

Segmentation Based Image Scanning

The submitted paper deals with separate scanning of individual image segments. A new image processing approach based on image segmentation and segment scanning is presented. The resulting individual segments 1-dimensional representation provides higher neighbor pixel similarity than the 1-dimensional representation of the original image. This increased adjacent pixel similarity was achieved even without application of different recursive 2-dimensional scanning methods [4], such as Peano-Hilbert scanning method [1]. The resulting 1-dimensional image representation provides a good base for applying lossless compression methods, such as the entropic coding. The paper contains also results analysis of the traditional method scanned segment pixels and adjacent pixel differences from the entropy point of view. As these results indicate the lossy compression methods could be applicable using this approach as well and might improve the final results as confirmed by simple prediction algorithm results presented in this paper. More complex and sophisticated lossy compression algorithms application will be a part of the future work

FPGA implementation of a predictive vector quantization image compression algorithm for image sensor applications

This paper presents a hybrid image compression scheme based on a block based compression algorithm referred to as Vector Quantization (VQ) combined with the Differential Pulse Code Modulation (DPCM) technique. The proposed image compression technique called the PVQ scheme results in enhanced image quality as compared to the standalone VQ. The generated codebooks for the PVQ scheme are more robust for image coding than that of the VQ. This made our system a suitable candidate for developing on chip image sensor with integrated data compression processor. The proposed system was validated through FPGA implementation. The resulting implementation achieved good compression and image quality with moderate system complexity

Binary image compression using run length encoding and multiple scanning techniques

While run length encoding is a popular technique for binary image compression, a raster (line by line) scanning technique is almost always assumed and scant attention has been given to the possibilities of using other techniques to scan an image as it is encoded. This thesis looks at five different image scanning techniques and how their relation ship to image features and scanning density (resolution) affects the overall compression that can be achieved with run length encoding. This thesis also compares the performance of run length encoding with an application of Huffman coding for binary image compression. To realize these goals a complete system of computer routines, the Image, Scanning and Compression (ISC) System has been developed and is now avail able for continued research in the area of binary image compression

Neural Space-filling Curves

We present Neural Space-filling Curves (SFCs), a data-driven approach to infer a context-based scan order for a set of images. Linear ordering of pixels forms the basis for many applications such as video scrambling, compression, and auto-regressive models that are used in generative modeling for images. Existing algorithms resort to a fixed scanning algorithm such as Raster scan or Hilbert scan. Instead, our work learns a spatially coherent linear ordering of pixels from the dataset of images using a graph-based neural network. The resulting Neural SFC is optimized for an objective suitable for the downstream task when the image is traversed along with the scan line order. We show the advantage of using Neural SFCs in downstream applications such as image compression. Code and additional results will be made available at https://hywang66.github.io/publication/neuralsfc