Raja Balasubramanian

Method for quantifying the color gamut of an output device

A technique is proposed for estimating the surface of the color gamut of an output device, in 3D colorimetric space. The method employs a modified convex hull algorithm. This approach is shown to be more general, and more accurate, than existing techniques. Simple numerical metrics are derived from this surface description: namely the gamut volume in 3D space; and the percentage of colors from the Pantone Matching System which fall within the gamut.

Sequential scalar quantization of color images

An efficient algorithm for color image quantization is proposed based on a new vector quantization technique that we call sequential scalar quantization. The scalar components of the 3-D color vector are individually quantized in a predetermined sequence. With this technique, the color palette is designed very efficiently, while pixel mapping is performed with no computation. To obtain an optimal allocation of quantization levels along each color coordinate, we appeal to the asymptotic quantization theory, where the number of quantization levels is assumed to be very large. We modify this theory to suit our application, where the number of quantization 1evels is typically small. To utilize the properties of the human visual system (HVS), the quantization is performed in a luminance-chrominance color space. A luminance-chrominance weighting is introduced to account for the greater sensitivity of the HVS to luminance than to chrominance errors. A spatial activity measure is also incorporated to reflect the increased sensitivity of the HVS to quantization errors in smooth image regions. The algorithm yields high-quality images and is significantly faster than existing quantization algorithms.

Sequential scalar quantization of vectors: an analysis

Proposes an efficient vector quantization (VQ) technique called sequential scalar quantization (SSQ). The scalar components of the vector are individually quantized in a sequence, with the quantization of each component utilizing conditional information from the quantization of previous components. Unlike conventional independent scalar quantization (ISQ), SSQ has the ability to exploit intercomponent correlation. At the same time, since quantization is performed on scalar rather than vector variables, SSQ offers a significant computational advantage over conventional VQ techniques and is easily amenable to a hardware implementation. In order to analyze the performance of SSQ, the authors appeal to asymptotic quantization theory, where the codebook size is assumed to be large. Closed-form expressions are derived for the quantizer mean squared error (MSE). These expressions are used to compare the asymptotic performance of SSQ with other VQ techniques. The authors also demonstrate the use of asymptotic theory in designing SSQ for a practical application (color image quantization), where the codebook size is typically small. Theoretical and experimental results show that SSQ far outperforms ISQ with respect to MSE while offering a considerable reduction in computation over conventional VQ at the expense of a moderate increase in MSE.

Color-image quantization with use of a fast binary splitting technique

We investigate an efficient color-image quantization technique that is based on an existing binary splitting algorithm [ IEEE Trans. Signal Process. 39, 2677 ( 1991)]. The algorithm sequentially splits the color space into polytopal regions and picks a palette color from each region. As originally proposed, the complexity of this algorithm is a function of the image size. We introduce a fast histogramming step so that the complexity will depend only on the number of distinct image colors. Data structures are employed that permit the storage of a full-color histogram at moderate memory cost. In addition, we apply a prequantization step that reduces the number of initial image colors while preserving image quality along visually important color coordinates. Finally, we incorporate a spatial-activity measure to reflect the increased sensitivity of the human observer to quantization errors in smooth image regions. This technique preserves the quantitative and qualitative performance of the original binary splitting algorithm while considerably reducing the computation time.

Refinement of printer transformations using weighted regression

Printer characterization and color correction are often complex transformations, and are derived with numerous measurements or printer models. There are many sources of errors in these transforms, including inaccuracies in lookup table approximation, errors in the printer model, noise in the data, and spatial and temporal non-uniformities in the printer. A method is proposed to increase the accuracy of an existing printer transform with a relatively small number of refinement measurements. A weighted linear least-squares regression technique is used to improve the fit of the printer response to the refinement data. The hypothesis is that a locally linear transform can adequately capture the difference between the true printer transform and its approximation. In contrast to existing approaches that only refine the individual C, M, Y, K responses, the proposed method attempts to account for cross-colorant interactions by using mixed colors in the refinement set. Furthermore, the refinement data is not restricted to lying on a regular grid, and can be freely chosen based on any a priori knowledge about the printer. The approach is tested for two related transforms: the characterization transform which maps CMYK to L*a*b*; and its inverse, the color correction transform that maps L*a*b* to CMYK. Results show an improvement in transform accuracy with a relatively small number of measurements.

Model-based color image quantization

In this paper, we propose a new technique for halftoning color images. Our technique parallels recent work in model-based halftoning for both monochrome and color images; we incorporate a human visual model that accounts for the difference in the responses of the human viewer to luminance and chrominance information. Thus, the RGB color space must be transformed to a luminance/chrominance based color space. The color transformation we use is a linearization of the uniform color space L*a* b* which also decouples changes between the luminance and chrominance components. After deriving a tractable expression for total- squared perceived error, we then apply the method of Iterated Conditional Modes (ICM) to iteratively toggle halftone values and exploit several degrees of freedom in reducing the perceived error as predicted by the model.

Colorimetric modeling of binary color printers

Colorimetric device models play an important role in achieving consistent and accurate color reproduction among digital output devices. Models based on the Neugebauer (1937) mixing equations are examined for halftone color printers. Spectral information, and the Yule-Neilsen (1951) correction for light scattering, are incorporated into the models. A cellular approach is examined as a tradeoff between model accuracy and complexity. Two halftone screen orientations are discussed: the rotated or random dot; and the dot-on-dot configuration. Results show that the models can predict the printer response with acceptable accuracy.

New approach to palette selection for color images

We apply the vector quantization algorithm proposed by Equitz to the problem of efficiently selecting colors for a limited image palette. The algorithm performs the quantization by merging pairwise nearest neighbor (PNN) clusters. Computational efficiency is achieved by using k- dimensional trees to perform fast PNN searches. In order to reduce the number of initial image colors, we first pass the image through a variable-size cubical quantizer. The centroids of colors that fall in each cell are then used as sample vectors for the merging algorithm. Tremendous computational savings is achieved from this initial step with very little loss in visual quality. To account for the high sensitivity of the human visual system to quantization errors in smoothly varying regions of an image, we incorporate activity measures both at the initial quantization step and at the merging step so that quantization is fine in smooth regions and coarse in active regions. The resulting images are of high visual quality. The computation times are substantially smaller than that of the iterative Lloyd-Max algorithm and are comparable to a binary splitting algorithm recently proposed by Bouman and Orchard.

New results in color image quantization

We investigate an efficient color image quantization technique that is based upon an existing binary splitting algorithm. The algorithm sequentially splits the color space into polytopal regions and picks a palette color from each region. At each step, the region with the largest squared error is split along the direction of maximum color variation. The complexity of this algorithm is a function of the image size. We introduce a fast histogramming step so that the algorithm complexity will depend only on the number of distinct image colors, which is typically much smaller than the image size. To keep a full histogram at moderate memory cost, we use direct indexing to store two of the color coordinates while employing binary search to store the third coordinate. In addition, we apply a prequantization step to further reduce the number of initial image colors. In order to account for the high sensitivity of the human observer to quantization errors in smooth image regions, we introduce a spatial activity measure to weight the splitting criterion. High image quality is maintained with this technique, while the computation time is less than half of that of the original binary splitting algorithm.

Printer model for dot-on-dot halftone screens

A printer model is described for dot-on-dot halftone screens. For a given input CMYK signal, the model predicts the resulting spectral reflectance of the printed patch. The model is derived in two steps. First, the C, M, Y, K dot growth functions are determined which relate the input digital value to the actual dot area coverages of the colorants. Next, the reflectance of a patch is predicted as a weighted combination of the reflectances of the four solid C, M, Y, K patches and their various overlays. This approach is analogous to the Neugebauer model, with the random mixing equations being replaced by dot-on-dot mixing equations. A Yule-Neilsen correction factor is incorporated to account for light scattering within the paper. The dot area functions and Yule-Neilsen parameter are chosen to optimize the fit to a set of training data. The model is also extended to a cellular framework, requiring additional measurements. The model is tested with a four color xerographic printer employing a line-on-line halftone screen. CIE L*a*b* errors are obtained between measurements and model predictions. The Yule-Neilsen factor significantly decreases the model error. Accuracy is also increased with the use of a cellular framework.