James M. Kasson

An analysis of selected computer interchange color spaces

Important standards for device-independent color allow many different color encodings. This freedom obliges users of these standards to choose the color space in which to represent their data. A device-independent interchange color space must exhibit an exact mapping to a colorimetric color representation, ability to encode all visible colors, compact representation for given accuracy, and low computational cost for transforms to and from device-dependent spaces. The performance of CIE 1931 XYZ, CIELUV, CIELAB, YES, CCIR 601-2 YCbCr, and SMPTE-C RGB is measured against these requirements. With extensions, all of these spaces can meet the first two requirements. Quantizing error dominates the representational errors of the tested color spaces. Spaces that offer low quantization error also have low gain for image noise. All linear spaces are less compact than nonlinear alternatives. The choice of nonlinearity is not critical; a wide range of gammas yields acceptable results. The choice of primaries for RGB representations is not critical, except that high-chroma primaries should be avoided. Quantizing the components of the candidate spaces with varying precision yields only small improvements. Compatibility with common image data compression techniques leads to the requirement for low luminance contamination, a property that compromises several otherwise acceptable spaces. The conversion of a device-independent representation to popular device spaces by means of trilinear interpolation requires substantially fewer lookup table entries with CCIR 601-2 YCbCr and CIELAB.

Performing color space conversions with three-dimensional linear interpolation

Three-dimensionalinterpolation is suitable for many kinds of color space transformations. We examine and analyze several linear interpolation schemes-some standard, some known, and one novel. An interpolation algorithm design is divided into three parts: packing (filling the space of the input variable with sample points), extraction (selecting from the constellation of sample points those appropriate to the interpolation of a specific input point), and calculation (using the extracted values and the input point to determine the interpolated approximation to the outputpoint). We focus on regular (periodic) packing schemes. Seven principles govern the design of linear interpolation algorithms: 1) Each sample point should be used as a vertex of as many polyhedra as possible; 2) the polyhedra should completely fill the space; 3) polyhedra that share any part of a face must share the entire face; 4) the polyhedra used should have the fewest vertices possible; 5) polyhedra should be small; 6) in the absence of information about cuivature anisotropy, polyhedra should be close to regular in shape; and 7) polyhedra should be of similar size. A test for interpolation algorithm performance in performing actual color space conversions is described, and results are given for an example color space conversion using several linear interpolation methods. The extractions from cubic, body-centered-cubic, and face-centered-cubic lattices are described and analyzed. The results confirm Kanamoris claims for the accuracy of PRISM interpolation; it comes close to the accuracy of trilinear interpolation with roughly three-quarters the computations. The results show that tetrahedral interpolation, with close to half the computational cost of tnlinear interpolation, is capable of providing better accuracy. Of the tetrahedral interpolation techniques, one diagonal extraction from cubic packing is useful as a general-purpose color space interpolator...

Tetrahedral interpolation technique for color space conversion

Three-dimensional interpolation is often employed to minimize calculations when approximating mathematically defined complex functions or producing intermediate results from sparse empirical data. Both situations occur when converting images from one device- independent color space to another, or converting information between device-dependent and device-independent color spaces; this makes three-dimensional interpolation an appropriate solution to many kinds of color space transformations. Interpolation algorithms can be analyzed by considering them as consisting of three parts: packing, in which the domain of interest of the input space is populated with sample points; extraction, which consists of selecting the sample points necessary to approximate the function for a particular input value; and calculation, which accepts the input point and the extracted points and carries out calculations to approximate the function. Those algorithms that extract four points and perform tetrahedral interpolation yield the fewest calculations. The paper presents a test for interpolation algorithm accuracy, and provides a normalization which allows various packing and extraction schemes to be compared. When subjected to the normalized accuracy test, different packing and extraction schemes yield different accuracies. The paper describes a packing and an extraction algorithm that yields accurate results for many conversions. The performance of this scheme is compared to that of several well-known packing and extraction algorithms.

Printing CIELAB images on a CMYK printer using trilinear interpolation

The Color Rendering project at IBM Almaden Research Center is examining the problem of how to display and print quality color images. For this work we need a printer calibrated to a device independent color space. In this paper, we describe a system for printing CIELAB images on a CMYK printers, and focus particularly on calibration methods. We use tri-linear interpolation to convert CIELAB colors to CMY or CMYK colorants. We obtain the interpolation table by inverting a tetrahedral linear interpolation of a calibration table constructed by measuring printed color patches. Since tetrahedral interpolation has a simple analytical inverse, we can produce the inverted table much more quickly than with the numerical methods needed to invert a multilinear interpolation, even though we have to measure more patches to obtain the same accuracy. To cover the full printer gamut, we found it necessary to add some out-of-gamut entries to the inverted interpolation table. These entries must be obtained by extrapolation, and increase the errors interpolating colors on and near the gamut surface. To date we have calibrated a DuPont 4Cast to print CIELAB colors using CMY colorants. We discuss our results with this calibration, how we propose to add black, and how we fit gamut mapping into the processing.© (1992) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Tetrahedral interpolation algorithm accuracy

Three-dimensional interpolation can minimize calculations when converting images from one device-independent color space to another or converting information between device-dependent and device-independent color spaces; this makes 3D interpolation a suitable way to implement many kinds of color space transformations. This paper analyzes trilinear interpolation and several tetrahedral interpolation schemes that extract data from a cubical packing of space, including a five-tetrahedron scheme proposed by Kanamori and Kotera, a six-tetrahedron method due to Clark, and three variations on the Clark arrangement. Also analyzed are two versions of the disphenoid extraction from the body-centered-cubic packing proposed by Kasson, Plouffe, and Nin, and the PRISM method reported by Kanamori, et al. The test for interpolation algorithm performance of the earlier paper is applied to a large set of color space conversions and lattice granularities, allowing meaningful conclusions about average and worst-case performance.

Requirements for computer interchange color spaces

Computer systems thatprocluce color images, usually consist ofcombinations ofhardware and software components that perform different functions, such as capturing, synthesizing or editing images, incorporating images into documents, proofing, and rendering results. Images, and the documents containing them, must be stored temporarily or archivally, and transmitted from component to component. Users will be able to operate such systems more conveniently and flexibility if the parts communicate with each other using a standard interchange format, allowing any conforming module to communicate with any other. This paper discusses the requirements for such an interchange color space, comparing them to some ofthe criteria used to measure traditional color spaces. Any computer interchange space should employ the principles of colorimetry to provide deviceindependence, which is necessary if negotiation between components is to be avoided. Other requirements are accuracy and computational efficiency of transforms to and from device-dependent and internationally standard spaces, ability to represent all visible colors, maximizing the amount of space occupied by the most likely image color gamuts, and robustness against quantization and roundoff errors. This paper proposes ways to measure the performance of color spaces against the defined requirements and applies the tests to several well-known color spaces.

Efficient chromaticity-preserving sharpening of RGB images

The conventional method of performing spatial filtering of RGB images is to subject each plane to the same processing, usually convolution with a filter kernel. Filtering is commonly used in the processing of photographic or photo-realistic images to sharpen or blur images, and to produce aesthetically-pleasing effects. For image sharpening, the technique of subjecting each plane to the same processing produces objectionable color errors in some circumstances, and that techniques which convert the image to a color space that separates luminance from chrominance and performing the filtering only on the luminance component can produce better results. The problem with this approach has been the computational cost of making the transformation, first to the luminance- chrominance space, and back to RGB. This paper presents an algorithm which operates on an RGB image and provides results which are free from chromaticity changes. It achieves these results with fewer computations than filtering the luminance component in a luminance-chrominance color space. In fact, the computations required are usually simpler than processing each RGB plane.