The digital representation of an image requires a very large number of bits. The goal of image coding is to reduce this number, as much as possible, and reconstruct a faithful duplicate of the original picture. Early efforts in image coding, solely guided by information theory, led to a plethora of methods. The compression ratio, starting at 1 with the first digital picture in the early 1960s, reached a saturation level around 10:1 a couple of years ago. This certainly does not mean that the upper bound given by the entropy of the source has also been reached. First, this entropy is not known and depends heavily on the model used for the source, i.e., the digital image. Second, the information theory does not take into account what the human eye sees and how it sees. Recent progress in the study of the brain mechanism of vision has opened new vistas in picture coding. Directional sensitivity of the neurones in the visual pathway combined with the separate processing of contours and textures has led to a new class of coding methods capable of achieving compression ratios as high as 70:1. Image quality, of course, remains as an important problem to be investigated. This class of methods, that we call second generation, is the subject of this paper. Two groups can be formed in this class: methods using local operators and combining their output in a suitable way and methods using contour-texture descriptions. Four methods, two in each class, are described in detail. They are applied to the same set of original pictures to allow a fair comparison of the quality in the decoded pictures. If more effort is devoted to this subject, a compression ratio of 100:1 is within reach.

Second-generation image-coding techniques

We introduce the Adaptive Hough Transform, AHT, as an efficient way of implementing the Hough Transform, HT, method for the detection of 2-D shapes. The AHT uses a small accumulator array and the idea of a flexible iterative "coarse to fine" accumulation and search strategy to identify significant peaks in the Hough parameter spaces. The method is substantially superior to the standard HT implementation in both storage and computational requirements. In this correspondence we illustrate the ideas of the AHT by tackling the problem of identifying linear and circular segments in images by searching for clusters of evidence in 2-D parameter spaces. We show that the method is robust to the addition of extraneous noise and can be used to analyze complex images containing more than one shape.

The Adaptive Hough Transform

We present a method for the classification of 2-D partial shapes using Fourier descriptors. We formulate the problem as one of estimating the Fourier descriptors of the unknown complete shape from the observations derived from an arbitrarily rotated and scaled shape with missing segments. The method used for obtaining the estimates of the Fourier descriptors minimizes a sum of two terms; the first term of which is a least square fit to the given data subject to the condition that the number of missing boundary points is not known and the second term is the perimeter2/area of the unknown shape. Experiments with synthetic and real boundaries show that estimates closer to the true values of Fourier descriptors of complete boundaries are obtained. Also, classification experiments performed using real boundaries indicate that reasonable classification accuracies are obtained even when 20-30 percent of the data is missing.

Classification of Partial 2-D Shapes Using Fourier Descriptors

Review of shape coding techniques

Enhancement of low bit-rate coded images using edge detection and estimation

This paper describes a coding strategy which stores digital images in terms of their contours. The data in the original raw image is reorganised into a set of 1-d trajectories and these are normalised in length and approximated by low rank models. It is the coefficients of these models which are retained. The second order statistical information is used to derive a vector codebook containing standard sets of coefficients, and each contour is allocated the codeword of the nearest standard vector. In this way a codebook of generating functions for standard shapes is obtained. The problems of non closing contours are addressed along with interpolation methods to produce a reconstructed image from a contoured image.

Contour coding of images

In this paper we derive two algorithms for estimating concentrations of a known chemical compound from compressed measurements of a hyperspectral image (HSI). It is assumed that each resolved pixel in a scene contains a chemical of known spectral signature, at an unknown concentration. The problem is to estimate the concentration directly from the compressed measurements. Estimated concentrations are either displayed or used as detection scores in a threshold test for presence or absence of chemical. In the first algorithm we use matched filtering and ℓ1 regularization to extract an image of concentrations, directly from compressed data. In the second we model the image of concentrations in a fixed-resolution subspace of the 2D Haar wavelet domain, estimate its parameters in this space, and reconstruct the image of concentrations at a macro-pixel resolution. We evaluate our algorithms by applying them to several long-wave infrared (LWIR) HSI data sets, either synthetically generated or recorded by Physical Sciences Inc. Synthetically-generated data is compressed with a mathematically-defined linear compressor; real HSI data is compressed with PSI’s Digital Micromirror Device (DMD), which is a physical implementation of a mathematically-defined compressor; Fabry-Perot data is raw HSI data recorded by PSI, which is then compressed with a mathematically-defined compressor. We demonstrate for these data sets that estimating concentrations through matched filtering and ℓ1 inversion of compressed measurements yields detection performance that is as good as previously proposed methods that first reconstruct a hyperspectral data cube from compressed data, and then estimate or detect chemical concentrations. The proposed methods save on memory and computation. We demonstrate that detection performance is maintained when resolving concentration maps at a lower resolution, so long as the resolution is not too low.

Estimating chemical concentrations from compressed hyperspectral images

An environmentally hardened compressive sensing hyperspectral imager (CS-HSI) operating in the long wave infrared (LWIR) has been developed for low-cost, standoff, wide area early warning of chemical vapor plumes. The CS-HSI employs a single-pixel architecture achieving an order of magnitude cost reduction relative to conventional HSI systems and a favorable pixel fill factor for standoff chemical plume imaging. A low-cost digital micromirror device modified for use in the LWIR is used to spatially encode the image of the scene; a Fabry-Perot tunable filter in conjunction with a single element mercury cadmium telluride photo-detector is used to spectrally resolve the spatially compressed data. A CS processing module reconstructs the spatially compressed spectral data, where both the measurement and sparsity basis functions are tailored to the CS-HSI hardware and chemical plume imaging. An automated target recognition algorithm is applied to the reconstructed hyperspectral data employing a variant of the adaptive cosine estimator for detection of chemical plumes in cluttered and dynamic backgrounds. The approach also offers the capability to generate detection products in compressed space with no CS reconstruction. This detection in transform space can be performed with a computationally lighter minimum variance distortionless response algorithm, resulting in a bandwidth advantage that supports efficient search and confirm modes of operation.

L. Scharf

Papers

Contour coding of images

Estimating chemical concentrations from compressed hyperspectral images

Compressive sensing hyperspectral imager in the LWIR for chemical plume detection