R. Victor Klassen

Comparison of two image quality models

In recent years a number of different vision models have been proposed to assist in the evaluation of image quality. However, there have been few attempts to independently evaluate these models and to make comparisons between them. In this paper we first summarize the work that has been done in image quality modeling. We then select two of the leading image quality models, the Daly Visible Differences Predictor and the Sarnoff Visual Discrimination Model, for further study. We begin by describing our implementation, which was done from the published papers, of each of the models. We next discuss the similarities and the differences between the two models. The paper ends with a summary of the important advantages of each approach. The comparison of these two models is presented in the context of our research interests which are image quality evaluation for both computer imaging and computer graphics tasks. The paper includes illustrations drawn from these two areas.

Integer forward differencing of cubic polynomials: analysis and algorithms

Two incremental cubic interpolation algorithms are derived and analysed. Each is based on a known linear interpolation algorithm and modified for third order forward differencing. The tradeoff between overflow avoidance and loss of precision has made forward differencing a method which, although known to be fast, can be difficult to implement. It is shown that there is one particular family of curves which represents the worst case, in the sense that if a member of this family can be accurately drawn without overflow, then any curve which fits in the bounding box of that curve can be. From this the limitations in terms of step count and screen resolution are found for each of the two algorithms.

Exact integer hybrid subdivision and forward differencing of cubics

Forward differencing is widely used to generate rapidly large numbers of points at equally space parameter values along a curve. A failing of forward differencing is the tendency to generate many extraneous points for curves with highly nonuniform parameterizations. A key result is presented and proven, namely, that a few levels of subdivision, prior to initialization for forward differencing, can improve substantially the quality of the step size estimate, resulting in very few extra points. The initial subdivisions can be done without loss of the exact integer precision available in forward differencing. For small numbers of points—a common occurrence in fonts—exact subdivision is even faster than exact forward differencing. When exact subdivision is used in conjunction with a previously presented exact forward-differencing algorithm, arbitrary cubic curves may be rendered with 32-bit arithmetic and guaranteed single-pixel accuracy, in a grid with an address space as large as 0…7281, with no two generated points greater than one pixel apart. This is more steps than previously possible. Previous discussions of rendering using subdivision have concentrated not on distance but on straightness estimates, whereby subdivision can be stopped once a subcurve can be drawn safely using its polygonal approximation. In this article, bounds are also derived on the size of the control polygon after multiple levels of subdivision: these are used to determine bounds on the number of steps required for differencing. It is shown that any curve whose rasterization fits in a space of ω pixels requires no more than 9ω steps.

Correcting for short-range spatial non-linearities of CRT-based output devices

Most graphical output devices exhibit what has been termed spatial non-linearity: the effect of se tting two adjacent pixels to a given value is not the same as the sum of the effects of setting those two pixels to the same value in isolation: checkerboards of different frequencies do not have the same apparent luminance. We present a method applicable to bit-mapped devices for compensating for short-range spatial non-linearity in error-diffused images. The modification to error diffusion is such that it can be used with any error diffusion technique. In essence, it consists of finding the influence of the neighbouring (output) pixels when making the decision of whether to turn on a given pixel, and passing errors computed accordingly.

A note on integer subdivision of NURBS

In a recent article [1], Anantakrishnan and Piegl suggest an approximate method for integer subdivision of rational or nonrational splines. Herein is an analysis of the errors inherent in the approximation.

Two-dimensional vector field visualization by halftoning

Digital halftoning is a technique for converting an image with multiple levels of grey into a bi-level (bitmap) image, typically in preparation for printing on paper. It is standard practice to “optimize” the halftoning process to reduce the visibility of artifacts that appear as textures within what should be a region of uniform or slowly varying intensity. This paper describes a method of manipulating the halftoning process to cause the texture to give an indication of field direction, while the field magnitude is displayed using the intensity.

A SIMD parallel trapezoid rasterization algorithm

Abstract An algorithm for the rasterization of trapezoids on the Connection Machine TM (CM) is described. The input consists of an array of trapezoids, with two horizontal sides, arranged with one trapezoid per processor. (Unless otherwise indicated, “processor” should be taken to mean virtual processor.) Each trapezoid is converted to an edge record and the edge records are then distributed to enough processors so that each processor is responsible for one scanline of one trapezoid. Each processor computes a scan record for its scanline, and the scan records are then distributed to enough processors so that one processor is responsible for a single pixel. Final interpolation of position, and possibly shading information, is performed in parallel for all pixels thus created, and the pixels are then broadcast into a frame buffer array, with depth comparisons being performed at the receiving end to ensure that the nearest pixel appears in the array. The Connection Machine-specific features used by the algorithm are logarithmic time cumulative summing, general communication with comparisons for collision arbitration, and virtual processor sets. Performance is similar to that of good graphics workstations. The intended application is to display data already resident in the machine as the result of some previous computation, when a high-performance graphics workstation is not available.

Color difference metrics and surround effects: preliminary results

Whereas both the CMC color difference metric and CIE94 show a considerable dependence on chroma, our measurements of contrast sensitivity show little or no such dependence. That is, the sensitivity to spatial variations in lightness, chroma and hue do not appear to depend on chroma, at least not to an extent greater than inter-observer variability. A key difference between a contrast sensitivity experiment and a color matching experiment is that the background color is the former is of necessity the mean color of the grating, whereas the background in the latter is typically a neutral gray of specified reflectivity or luminance. Goodman hypothesized that the chroma dependence in CMC and CIE94 may result from distance from background, rather than distance from neutral; the experiments reported here test that hypothesis. Results are only preliminary: a single combination of hue and lightness was used throughout the experiments, however they indicated at least partial agreement with Goodmans hypothesis.

Resolution and bit depth: how much is enough?

We describe results of experiments studying the tradeoff between resolution and bit depth. Images in the experiments were printed on a high resolution imagesetter, eliminating most, if not all, device effects. They were first converted from PostScript to antialiased rasters at one of a set of resolutions, then converted from 8 bit to n bits for some value of n less than 8. Before printing, they were converted back to 8 bits and scaled up to printer resolution, then halftoned for printing. We were measuring human response to a system that had a bandwidth bottleneck somewhere upstream of the printer, and sophisticated resampling and halftoning at the printer itself. The images, typical of those used for critical evaluation of hard copy, contained text, analytical test targets, synthetic graphics and pictorial images. We found bit depths and resolutions beyond which no further improvement was observed, typically somewhat higher limits than previously believed. We also compared methods of font hinting for antialiased text, and found that font hinting improves text only at one bit per pixel, degrading it at higher bit depths.

Sampling locations and visual difference predictors

Visual difference predictors accept two imags as input, performed some processing, and produce a single image as output. The output image represent a map of the visibility of differences between the two input images. In practical applications, input images are received at whatever resolution is convenient for the application, and viewing distances are as appropriate for the task at hand. To match retinal sampling rates, the images are typically filtered and down-sampled. Given that the typically employed optical point spread functions do not completely remove high frequency information, we ask whether, and to what extent high frequency leakage leads to aliasing. In this paper we explore the amount of aliasing possible in our implementation of the Sarnoff Visual Discrimination Model, and describe a modification that uses a sampling grid similar to the Poisson disk distribution. We then compare the result of this sampling to that of the unmodified model.