<title>Intensity Mappings: Linearization, Image-Based, User-Controlled</title>

Abstract

Abstract The objective of intensity mappings, functions from recorded intensity to displayed intensity, is to provide contrast in the display of features of interest in images where these features appear as regions of increased or decreased intensity. Three component objectives of such mappings can be identified: 1) device linearization, 2) emphasis of contrast in commonly occurring and accurately measured intensities, and 3) user-controlled mapping based on the importance of features. Mappings of type 1, which immediately precede the display device, are designed to modify the device so that equal changes in the driving intensity value are equally perceivable. The importance of this mapping will be demonstrated, and the argument that by itself this mapping must improve displayed quality will be refuted. A method of measuring the JND curve and of calculating this mapping from it will be discussed. A method for automatic determination of a mapping of type 2 consisting of a nonstationary modification of Cormack's mean pixel uncertainty minimization method [Phys. Med. Biol. ^(2)] will be presented. Methods for user control in the determination of mappings of type 3 will be briefly discussed.The ProblemThe display of intensity-varying images is a common requirement in such diverse areas as medicine, astronomy, and satellite imagery, to mention just a few. These images are two- dimensional distributions of a single intensity variable, and features to be seen are areas of increased or decreased intensity. The images are created by a detection device or by an processing or construction system and are first recorded as a two-dimensional distribution of some nonviewable intensity variable such as the density distribution of silver on film, the electrical time signal which can drive a video display, the track of magnetic strength on videotape, or the array of numeric intensities in a computer memory. We call this original image the recorded and its intensity variable the recorded intensity. The purpose of a display system is to transform a recorded into an viewable by a human in such a way that features of interest are detectable and characterizable and draw the observer's attention. The recorded intensity serves as a driving intensity for the display system, which transforms this driving intensity into a viewable intensity.We are concerned here with the performance of displays in transmitting contrast in recorded intensity, as opposed to their performance in transmitting spatial information as measured by properties such as resolution and geometric distortion. The images with which this paper is concerned are not ordinary pictures of scenes directly viewable b> tue eye but rather those like infra-red images of the earth and diagnostic medical images v.nich are made by measuring the two-dimensional distribution or projection of some physical parameter. With these images the objective is to discern abnormal increases or decreases in intensity, but unlike ordinary pictures of scenes, there is no concern for realism in the display of these images.Display devices have been developed to present these images using various mechanisms for presentation and various scales of viewable intensity. Among the presentation mechanisms have been visible display on a CRT, electrostatic plotting, film exposure by movable light sources, and film exposure by CRT. Among the viewable intensity scales have been grey- scale, half-tone, various pseudocolor scales, and apparent height, as well as various combinations of these.Given a viewable intensity scale, a critical choice determining the quality of display of a recorded is of the mapping between recorded intensity and viewable intensity. The objective of the mapping is to transmit sensitively that contrast in the recorded which contains the information required by the observer. It is with this mapping that this paper is concerned. The paper is an attempt to provide a clear framework in which the mapping can be designed and chosen.Strictly speaking, the intensity mapping that we wish to optimize is that between recorded intensity and intensity perceived by the viewer. As diagramed in figure 1 this mapping consists of three consecutively applied mappings: first, the mapping that we