Toward an automatic color calibration for 3D displays

This article considers the color correction of a 3D projection display installation. The system consists of a pair of projectors of the same model modified by INFITECGmbH such that they can be used for projection of 3D contents. The goal of this color correction is to reduce the difference between the two mo-dified projectors such as the color difference between them does not disturb the user. Two new approaches are proposed and compared with the Infitec expert correction. One is based on an objective colorimetric match, the other on the optimization of a transform considering the color difference between the two signals. Introduction The concept of 3D projection is not new, at the early age of photography already, photographers have experimented this principle by taking two pictures of the same scene to give another dimension to their image. Each taken picture corresponding to the same scene as if it was viewed for one by the left eye and for the other by the right eye. Today, 3D is becoming more and more popular in various domain (cinema, medical imaging, simulation, etc) and various technologies exist, requiring specific glasses (stereoscopic) or not (auto-stereoscopic) to see 3D content. The concept remains identical: displaying two images of a scene, one for the right eye and one for the left eye. From a colorimetric point of view, the case of an autostereoscopic display is simple: the same light source is used to project/display images to both eyes. On the other hand, a stereoscopic display needs two projection systems and glasses (the spectacle glasses consist of a couple of filters that scatter the signal in two, one for each eye) to display 3D images. In some technologies, two different sets of primaries are necessary. Improvements in filter technology has allowed to reduce the difference between the primaries of a pair of projectors [1], filters can have narrow band sizes (e.g. the use of two narrow red filters on the projectors decreases the difference between the two red primaries). But still, the difference is perceivable when an image or a film is observed without glasses: one projector is usually said to be reddish and the other greenish. In our work, we used projectors modified by INFITECGmbH. The projectors are modified with filters that are introduced in each projector to divide each primary red (R), green (G) and blue (B) in a reddish (or greenish) projector. The glasses are developed in parallel such that each spectacle has filtering properties according to the filters introduced in each projector. As a result our projection system is made of two projectors of very near set of primaries, near according to wavelength peaks difference between the red, green and blue primaries. The colorimetric properties of such a system has been studied [2], but no color correction is proposed yet, as far as we know, except the individual calibration of each projector followed by a manual expert correction. We continue this article by presenting in detail this projection system and showing how the projectors primaries are modified with the filters. Based on this, we study different approaches for reducing the reddish and greenish effects. The first approach involves a manual process defined by INFITECGmbH (the common process). We then show how an objective correction can be set up to reach an automatic colorimetric equivalence. The third method consists in optimizing the transform to maximize the dynamic range while keeping the difference unnoticeable. Experimental setups Projection system and measurement A pair of modified JVC DLA-HD1 projectors constitutes our projection system. The light source is an Ultra-high pressure mercury lamp with three typical wavelength peaks for the three primaries. With a BLUE-Wave Spectrometer from StellarNet we measure the light reflected by our screen (a wall painted by slightly grayish color). The measurements are made on a spectral window of [190nm− 1150nm] with a resolution of 0.5nm, for our experiments we work only on the visible spectrum window of [400nm− 700nm] and each spectral reflectance measured is resampled to obtain a resolution of 1nm such that each reflectance is represented by a vector of 400 : 1 : 700= 301 discrete values. In a first step we project an image completely white (i.e. digital value c = [r g b] = [1 1 1] ), for the red projector alone, the green projector alone and the two projectors together and measure the light reflected on the screen for each of these configurations. The direct measured curves are displayed in Fig. 1, Fig. 2 and Fig. 3. In each figure the red curves correspond to the projector with red filter, the green curves to the projector with the green filter. Our reference white w is the combination of both projectors projecting their maximum intensity in the same time, this is showed in the same figures by the black curve. Similarly our reference black k is the measurement of both projectors projecting a black image. To illustrate the terms greenish projector and reddish projector in those figures we have superposed on the primaries curves the closest corresponding CIE color matching function (CMF) curves for the CIE 1931 standard observer , i.e the x̄(λ ) is displayed in Fig. 1 for the red primaries of both projectors. In these figures the CIE CMFs have been scaled such that we can observe how the peak of each function matches or not with the peak of each projector primary. Later, to compute colorimetric values of the displayed color from the various RGB digital values input, we normalize the spectral signal using the following formula: S = s−k w−k (1) 18th Color Imaging Conference Final Program and Proceedings 5 400 450 500 550 600 650 700 0 1 2 3 4 5 6 x 10 4 wavelength λ (nm) li g h t m e a s u re m e n t Red primary of both projectors white Pg Pr x bar Figure 1. Light measurements of white (both projectors projecting white), the red primaries for both greenish (in green) and reddish (in red) projectors and the x̄(λ ). 400 450 500 550 600 650 700 0 1 2 3 4 5 6 x 10 4 wavelength λ (nm) li g h t m e a s u re m e n t Green primary of both projectors white Pg Pr y bar Figure 2. Light measurements of white (both projectors projecting white), the green primaries for both greenish (in green) and reddish (in red) projectors and the ȳ(λ ). 400 450 500 550 600 650 700 0 1 2 3 4 5 6 x 10 4 wavelength λ (nm) li g h t m e a s u re m e n t Blue primary of both projectors white Pg Pr z bar Figure 3. Light measurements of white (both projectors projecting white), the blue primaries for both greenish (in green) and reddish (in red) projectors and the z̄(λ ). that includes an offset correction k and where s is the measure from our spectrometer. In the figure showing the light measurements of pairs of primaries we can observe the poor overlap be0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 chromaticity x c h ro m a ti c it y y Projectors primaries Figure 4. Primaries describing the projector gamuts in the chromaticity diagram. In red, the reddish projector, in Green the greenish. The projector resulting of the sum of them seen without 3D glasses is plotted in Black. tween the primaries which illustrates the sharpness of the filters. Also Fig. 4 displays the same information but in a chromaticity diagram and reveals the differences between the primaries, especially for the green channels. Study of displayable colors We project and measure ramps of red, green, blue and gray to evaluate the intensity response curve of each primary. For the future experiments in this article we approximate the response curve of each primary by a power function xγ = x1.8. The chromaticity values of each primaries are plotted for each projector in Fig. 5. This figure shows as well the gamut resulting in summing couple of primaries from both projectors and the common gamut between them. Binocular color correction As we can observed in the figures showing the spectral curves and chromaticity diagrams each projector presents a dominant tint. If the display is observed without glasses, the superposition of the full intensity images from both projectors should appear neutral/white to the human eye. However, the 3D effect appears while wearing the glasses. Looking at the image through one spectacle, one can easily perceive the dominant tint, the effect is decreased when the images arrive on each eye, but still the perceived image or color signal slightly deviates from the desirable color (especially for ’known’ colors such as white snow, blue sky, human skin, etc). We can face three cases: The difference is large enough to cause binocular color rivalry [4], or it is small enough to generate a binocular color fusion [5]. In the case of a color fusion, we can face two cases: either it can be disturbing, such as in the snow or blue sky example, either it is unnoticeable or at least not disturbing. The problem can be solved through a color correction that is similar to a gamut mapping problem: How to modify the color rendering of each projector such that the differences between the displayed colors are smaller so that the color difference between the perceived images are not disturbing? We limit this work to simple and practical approaches, thus we consider a linear transform of the original RGB values. We can define the correction on the original RGB values used to control 6 ©2010 Society for Imaging Science and Technology the projectors as follows: c = Mc (2) where M is a 3×3 correction matrix and c′ = [r′ g′ b′]T and c = [r g b] the corrected and original normalized RGB values. In this article we compare three approaches to evaluate the correction matrices (one for each projector): one approach controlled by the eyes of experts, one colorimetric objective transform and a third method that defines the transform in minimizing the colorimetric error while maximizing the resulting common gamuts. All approaches require to linearize the intensity response curve of the projector, such as in Eq.3. We approximated the response curve with a power function, finding a gamma value of 1.8 for our installation. cY = [rY gY bY ] T = c (3) The colorimetric value of a displayed color can then be approximated assuming the primaries chromaticity constancy and a perfect additive mixing system: C = PcY (4) with C = [X ,Y,Z] the tristimulus colorimetric values of the displayed color. And P the colorimetric transform associated to a projector such as: