Nitin Sampat

Chromaticity Matrix to Tristimulus Matrix Conversion for RGB Color Spaces–Even In the Dark

Two methods to transform primary chromaticities and white point into primary tristimulus values are examined and compared. One method appears in numerous places in the literature; we refer to this as the “familiar” method, and provide a novel interpretation of it. The second is much less well-known and is referred to as the “unfamiliar” method. Necessary and sufficient conditions for computing primary tristimulus values from their chromaticities are identified; in brief, the triangle in the (x , y) chromaticity diagram must have non-zero area. The computational burdens for the methods were compared; the familiar method required slightly more arithmetical operations. Two problems with the familiar method were identified: high potential for rounding error and the inability to contend with a non-luminous primary. The unfamiliar method is less prone to rounding error, and is able to contend with primaries on the alychne. It is recommended that the unfamiliar method be preferred. Symbols and Notation R, G, B: Radiometrically-linear red, green, and blue X , Y, Z : (CIE) tristimulus values Xn, Yn, Zn: Tristimulus values of color space’s white point XR, YR, ZR: Tristimulus values of color space’s red primary XG , YG , ZG ; XB , YB , ZB : Tristimulus values of color space’s green and blue primaries, respectively xR, yR, zR: Chromaticity coordinates of red primary xG , yG , zG ; xB , yB , zB : Chromaticity coordinates of green and blue primaries, respectively T: Matrix containing the tristimulus values of the primaries T̃: Matrix of tristimulus values of primaries, with each primary normalized to unit luminance C: Matrix containing the chromaticity coordinates of the primaries SR: Tristimulus sum for red primary (SR = XR+YR+ ZR) SG , SB : Tristimulus sums for green and blue primaries, respectively S: Matrix containing SR, SG , and SB on diagonal, zero elsewhere Some nomenclature This paper compares two methods for computing the tristimulus values of three primaries of specified chromaticity coordinates that result in a specified white point. That phrase, while accurate, is cumbersome. We shall simply refer to “the tristimulus values of the primaries” in the remainder of the paper. Introduction In certain color spaces, including sRGB, primaries are specified in terms of their chromaticity coordinates, together with the tristimulus values of a white point. [1, 2] Some image storage formats, including the Portable Network Graphic (PNG) format, offer the capability of similar specification of the chromaticity coordinates of the primaries in image metadata. [3] Knowing the primaries permits color management, interchange of data, and greater inter-operability. These benefits stem from the ability to transform from RGB into a common color space such as CIE XYZ. Stable-primary RGB color spaces and their primaries In color spaces such as sRGB, Adobe 1998 RGB, and DCI-P3, the tristimulus values produced are linearly related to the relative radiometric amplitudes of each primary, with the linear relation governed by the tristimulus values of each primary. A color space with this property is characterized as having stable primaries. [4] The discussion in this paper applies to stable-primary RGB color spaces whose primaries are defined by their chromaticity coordinates, together with the tristimulus values of the white point. It is possible to define the primaries of a stable-primary RGB color space in terms of their tristimulus values. However, because tristimulus values vary with white point luminance and chromaticity, and the physical means of producing color, such as phosphors, filters, organic light-emitting diodes or lasers are more directly tied to the chromaticity coordinates, it is customary to specify the primaries in terms of their chromaticity coordinates (which are, in theory, invariant with respect to changes in white point). Nevertheless, it is their tristimulus values, rather than their chromaticity coordinates, that are ultimately required for color management and related tasks. Conversion input and output The goal is to start with a white point and the chromaticity coordinates of the primaries, and determine the tristimulus values of the primaries needed to produce the specified white point. The tristimIS&T International Symposium on Electronic Imaging 2018 Color Imaging XXIII: Displaying, Processing, Hardcopy, and Applications 324-1 https://doi.org/10.2352/ISSN.2470-1173.2018.16.COLOR-324 This work is licensed under the Creative Commons Attribution 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/

Front Matter: Volume 8660

This PDF file contains the front matter associated with SPIE Proceedings Volume 8660, including the Title Page, Copyright Information, Table of Contents, and the Conference Committee listing.

Front Matter: Volume 8299

This PDF file contains the front matter associated with SPIE Proceedings Volume 8299, including the Title Page, Copyright Information, Table of Contents, and the Conference Committee listing.

Issues in implementing services for a wireless web-enabled digital camera

The competition in the exploding digital photography market has caused vendors to explore new ways to increase their return on investment. A common view among industry analysts is that increasingly it will be services provided by these cameras, and not the cameras themselves, that will provide the revenue stream. These services will be coupled to e- Appliance based Communities. In addition, the rapidly increasing need to upload images to the Internet for photo- finishing services as well as the need to download software upgrades to the camera is driving many camera OEMs to evaluate the benefits of using the wireless web to extend their enterprise systems. Currently, creating a viable e- appliance such as a digital camera coupled with a wireless web service requires more than just a competency in product development. This paper will evaluate the system implications in the deployment of recurring revenue services and enterprise connectivity of a wireless, web-enabled digital camera. These include, among other things, an architectural design approach for services such as device management, synchronization, billing, connectivity, security, etc. Such an evaluation will assist, we hope, anyone designing or connecting a digital camera to the enterprise systems.