Electronic distortion correction for multiple image layers Marco Winzker Uwe Rabeler Abstract — Images displayed by projection systems can experience geometric distortions. These dis- tortions can be compensated for by electronic correction, also called image warping. When the image that will be displayed is composed of several input sources, the different image layers have to be corrected independently from each other in order to achieve optimal image quality. A VLSI architec- ture for independent electronic correction of multiple image layers is proposed. Keywords — Display controller, scaling, warping, overlay, alpha-channel. 1 Introduction For image acquisition with an electronic camera, a scene in the real world is projected by a complex lens system on an image sensor and converted to an electronic signal. For image presentation using a projector, the electronic image information is presented on a digital display device, e.g., an LCD or DMD. Again, a lens system is used to project the image onto a screen or directly on the retina of an eye. In a camera as well as the projector, an optical system and an electronic system work closely together. Conse- quently, during the design of the electronic system the char- acteristics of the optical system and vice versa have to be considered. Furthermore, one system is able to compensate for the deficiencies of the other. Due to the advances in VLSI technology leading to increasing computing power for decreasing cost, it is the electronic system that can compen- sate more and more optical distortions. Optical distortions have been accepted for some appli- cations because they need only qualitative measurement and do not require geometric accuracy. For other applica- tions, e.g., image projection, geometric accuracy is not abso- lutely required but becomes a quality feature. A further range of applications really requires geometric accuracy. In this paper, we present a VLSI architecture for cor- recting a wide range of geometric distortions. The next sec- tion will present some sources of optical distortion and thus define the requirements for electronic correction. Section 3 explains how an output image is composed of different image layers. In Section 4, we present an architecture for electronic distortion correction and in Sections 5 discuss an ASIC implementation currently under development. 2 Sources of optical distortion Notation: Undistorted coordinates will be described as (x, y) and distorted coordinates as (x′, y′). The origin is the optical axis. Optical distortions have to be considered for image acquisition as well as for image presentation. For better readability, we will refer in the remainder of this text only to projection systems. Nevertheless, the results are also appli- cable for image acquisition. 2.1 Lens distortion Real lens systems are non-linear and introduce a radial shift to the position of the image pixel. This shift can result in a radial distortion called pincushion or barrel distortion. Fig- ure 1 shows the effect a barrel distortion has on a rectangu- lar grid of lines. Radial distortion can be described as a coordinate transformation. 1 The image information from position (x, y) is transformed to position (x′, y′) according to: (1) (2) ¢= + + + + + + x x k xd k xd k xd P x d P xy 1 2 2 4 3 6 1 2 2 2 2 2 ( ) , ¢= + + + + + + y y k yd k yd k yd P y d P xy 1 2 2 4 3 6 2 2 2 1 2 2 ( ) , Revised version of a paper presented at the 7th Asian Symposium of Information Display (ASID ‘02) held September 2–4, 2002, in Singapore. The authors are with Liesegang electronics GmbH, Mengendamm 12, 30171 Hannover, Germany; telephone +49-511-626-45-29, fax +49-511-626-45-80, e-mail: mwinzker@liesegang-electronics.com. U. Rabeler is now with sci-worx GmbH, Hannover, Germany.  Copyright 2003 Society for Information Display 1071-0922/03/1102-0309$1.00 FIGURE 1 — Barrel distortion of a rectangular grid of lines. Journal of the SID 11/2, 2003 309