The dominance of Poisson noise over signal independent Gaussian noise and other types has been demonstrated for commercial digital color cameras. We present a new method for estimating CIE colorimeric values in the presence of Poisson noise. The new methods use multidimensional look-up tables (MLUTs) and are easily adapted to the local statistics of the image. The methods are shown to perform better than common methods that are based on signal independent noise models.

In the design of a multiband imaging device, it is useful to model the response and performance of the instrument mathematically. Determining the device performance requires providing typical input to the device. Currently, there exist databases of hyperspectral images and spectral reflectance measurements that can provide limited input. In this document, methods for generating and modeling reflectance spectra are introduced. These artificial spectra can be useful as additional input to assess the performance of hyperspectal image processing algorithms and devices under specified statistical conditions.

With the proliferation of color display and input devices it has become less expensive to demonstrate and teach color image processing techniques. When teaching color image processing, it is important to emphasize that it is not a multichannel extension of monochrome image processing. This paper indicates the elements of color image processing and color image displays that every student and instructor should know. We give examples that can be used to illustrate these concepts.

In this paper, we look at the problem of spatially scaling color images. We focus on an approach that takes advantage of the human visual system's color spatial frequency sensitivity. The algorithm performs an efficient least-squares (LS) resolution conversion for the luminance channel and a low-complexity pixel replication/reduction in the chrominance channels. The performance of the algorithm is compared to a LS method in sRGB and CIELAB color spaces, as well as standard bilinear interpolation in sRGB space. The comparisons are made in terms of computational cost and color error in sCIELAB.

The proliferation of color devices and the desire to have them accurately communicate color information has led to a need for embedded systems that perform color conversions. A common method for performing color space conversions is to characterize the device with a multidimensional lookup table (MLUT). To reduce cost, many of the embedded systems have limited computational abilities. This leads to a need for the design of efficient methods for performing MLUT indexing and interpolation. This paper examines and compares two methods of MLUT indexing within embedded systems. The comparison is made in terms of colorimetric accuracy and computational cost.

With the proliferation of digital cameras, more consumers are faced with the problem of making color corrections to their pictures, while most picture editors allow some white point, or illuminant, correction and some enhancements, these methods work on the image, as a whole rather than on specific regions or colors. This work describes a simple method, that allows the user the ability to correct specific colors in specific locations in a picture. It is shown that relatively few sample colors are needed to produce a well-behaved interpolation in three-dimensional color spaces. A quantitative measure of performance is obtained by using the method to correct for illumination.

MLUTs used in color characterization require significant memory for embedded systems. Most tools that create device characterization maps, use MLUTs. For this reason, there is interest in approximating MLUT color characterization mappings with more compressed function approximation methods. In this document, artificial neural network approximations for MLUTs are investigated. Color accuracy, computational loads, and memory requirements are discussed.

Many researchers are working on various aspects of color imaging. However, it is apparent from the papers published that it is difficult for many of them to produce high quality color reproductions. While our previous work outlined the steps needed to produce calibrated color images, the problem of creating the programs to implement the process locally seems to be a serious problem. To surmount this final barrier, we have developed a web site that has the MATLAB programs necessary to characterize printers and produce high quality images.

To demonstrate the performance of color image processing algorithms, it is desirable to be able to accurately display color images in archival publications. In poster presentations, the authors have substantial control of the printing process, although little control of the illumination. For journal publication, the authors must rely on professional intermediaries (printers) to accurately reproduce their results. Our previous work describes requirements for accurately rendering images using your own equipment. This paper discusses the problems of dealing with intermediaries and offers suggestions for improved communication and rendering.

The concentration of most image processing courses is on the various algorithms used to alter an input image or data to produce a desired output image. Little effort is expended on teaching the appropriate display methods that are required to accurately demonstrate the effectiveness of the processing algorithms under investigation. This paper reviews the fundamentals of image display that every student should know before displaying the homework and project results that are assigned in those courses.

This paper reviews areas of active research in color image processing. Several open problems are mentioned and future directions for research are suggested. Topics discussed include: color perception, image recording, communication, and reproduction.

To demonstrate the performance of color image processing algorithms, it is desirable to be able to accurately display color images in archival publications. Our previous work (see IEEE Trans. Image Proc., vol.8, no.12, Dec. 1999), described requirements for accurately rendering images using your own equipment. This paper discusses the problems of dealing with intermediaries and offers suggestions for improved communication and rendering.

The mathematical formulation of calibrating color scanners is presented. The mapping from scanned values to colorimetric values is inherently nonlinear. Calibration required approximating this nonlinear mapping. Neural networks are particularly suited to this task. Performance using an artificial neural network generated LUT is compared to that achieved by other commonly used methods.

The mathematical formulation of calibrating color image reproduction and recording devices is presented. This formulation provides a foundation for future research in areas of characterization of devices and display of color images. The importance of calibration is demonstrated by real examples. The procedure outlined in this paper should become standard for displaying color images for the image processing community.

We introduce a method for multichannel restoration of images in which there is severely limited knowledge about the undegraded signal, and possibly the noise. We assume that we know the channel degradations and that there will be a significant noise reduction in a postprocessing stage in which multiple realizations are combined. This post-restoration noise reduction is often performed when working with micrographs of biological macromolecules. The restoration filters are designed to enforce a projection constraint upon the entire system. This projection constraint results in a system that provides an oblique projection of the input signal into the subspace defined by the reconstruction device in a direction orthogonal to a space defined by the channel degradations and the restoration filters. The approach achieves noise reduction without distorting the signal by exploiting the redundancy of the measurements.

The mathematical formulation of calibrating color image reproduction and recording devices is presented. This formulation provides a foundation for future research in areas of characterization of devices and display of color images. The procedure outlined in this paper should become standard for displaying color images for the image processing community.

To a significant degree, multimedia applications derive their effectiveness from the use of color graphics, images, and video. However, the requirements for accurate color reproduction and for the preservation of this information across display and print devices that have very different characteristics and may be geographically apart are often not clearly understood. This paper describes the basics of color science, color input and output devices, color management, and calibration that help in defining and meeting these requirements.

In this correspondence, the problem of designing color scanning filters for multi-illuminant color recording is considered. The filter transmittances are determined from a minimum-mean-squared orthogonal tristimulus error criterion that minimizes the color error in estimates obtained from noisy recorded data. Nonnegativity constraints essential for physical realizability are imposed on the filter transmittances. In order to demonstrate the significant improvements obtained, the resulting filters are compared with suboptimal filters reported in earlier literature.

We introduce a new method for initializing the multi-wavelet decomposition algorithm. The approach assumes that the input signal is contained within some well-defined subspace of L/sub 2/ (e.g. space of bandlimited functions). The initialization algorithm is the orthogonal projection of the input signal into the space defined by the multi-scaling function. Unlike an interpolation approach, the projection method will always have a solution. We provide examples and implementation details.

The CIE color matching functions, which are the foundation of computational color, are constructed and tabulated from experimental data by using various interpolations and smoothing. This work shows how the exact form of the mathematical operations used to construct the tabulated values can produce a bias in the computation of tristimulus values when used with sampled data obtained from various measuring instruments. The practical limitations caused by the bias are discussed.

We introduce a fast simple method for computing the real continuous wavelet transform (CWT). The approach achieves O(N) complexity per scale and the filter coefficients can be analytically obtained by a simple integration. Our method is to use P wavelets per octave and to approximate them with their oblique projection onto a space defined by a compact scaling function. The wavelet templates are expanded to larger sizes (octaves) using the two-scale relation and zero padded filtering. Error bounds are presented to justify the use of an oblique projection over an orthogonal one.

We introduce a general framework for the efficient computation of the continuous wavelet transform (CWT). The method allows arbitrary sampling along the scale axis, and achieves O(N) complexity per scale where N is the length of the signal. Our approach makes use of a compactly supported scaling function to approximate the analyzing wavelet. We derive error bounds on the wavelet approximation and show how to obtain any desired level of accuracy through the use of higher order representations. Finally, we present examples of implementation for different wavelets using polynomial spline approximations.

We introduce a projection based multi-channel restoration method which is useful in cases for which there is no a priori information about the input signal. The method is especially helpful in situations where a large number of specimens are later combined to achieve additional noise reduction. We describe the approach and discuss the problem of restoring electron micrographs. The method does require knowledge of the impulse response of the degradation. For this reason, the sensitivity of the approach to uncertainty in this degradation is investigated through simulation.

The effect of noise on the number of effective channels (color filters) used to record a color image is investigated. Transmittances of color filters are calculated that minimize the mean square error that occurs when estimating, from the recorded data, the colors in the image under a collection of viewing illuminants. Since the results indicate that a significant improvement in color correction accuracy is achieved by using four channels, there is good reason to consider using four-tuples for representation of colorimetric information.

The quality of color correction is dependent on the filters used to scan the image. This paper introduces a method of selecting the color filters using a priori information about the viewing illuminants. Color correction results using the derived filters are compared with color correction results using filters that are optimal for individual viewing and recording illuminants. The comparison is performed using the CIE PEL (L*a*b*) perceptual color difference measure. Applications of this work are found in the design of scanners, copiers, and television systems.

The reproduction of color images often requires color correction. The original image may have been recorded under one illumination while the reproduction is to be viewed under another or made to appear as if it were recorded under another. Since it is often the case that the original illumination is unknown to the image scientist, it is necessary to estimate. Two methods are presented for estimating the illuminant. The sensitivity of the methods to various assumptions is discussed.>