USE OF MATRICES FOR THE ADAPTATION OF VIDEO-BASED PHOTOGONIOMETRIC MEASUREMENTS TO A VARIABLE REFERENTIAL M. Andersen Solar Energy and Building Physics Laboratory LESO-PB, Swiss Federal Institute of Technology EPFL, CH – 1015 Lausanne, Switzerland ABSTRACT Digital video based luminance mapping systems require the establishment of a precise relation between the considered spatial referential and the associated pixel coordinates on the image, that may vary with the measurement conditions. In this paper, an adaptation of the image calibration according to the referential variations is proposed, based on the use of a set of matrices individually associated to each spatial coordinate. This approach is given through an application example on a recent digital imaging-based bi-directional photogoniometric device. RESUME Les systèmes de mesure de luminance basées sur l’imagerie numérique nécessitent une relation précise entre le référentiel considéré et les coordonnées des pixels associés sur l’image, qui peut varier avec les conditions de mesure. Ce papier propose une adaptation du calibrage de l’image en fonction des variations de référentiel, à l’aide d’un ensemble de matrices individuellement associées à chaque coordonnée spatiale. Cette approche est illustrée par une application sur un photogoniomètre bidirectionnel, basé sur l’imagerie numérique. INTRODUCTION A way to solve the problem of geometric calibration for a digital imaging based luminance- meter with variable referential appears when the latter undergoes geometric transformations that are analytically characterisable, even with non linear consequences on the image, provided that the relative positions of the camera and the filmed objects remain unchanged. The recognition and geometrical characterisation of objects on images aiming to deduce spatial parameters [1] is indeed not the subject treated here; this paper proposes a method to analyse images of a known geometric situation, whose investigation provides the expected information about a particular feature, bi-directional light transmission in our case, other photometric [2] or extended applications, and it is the observed feature that may be related to a well-known but variable referential. The exposed method consists of using a set of matrices, whose dimensions are equal to the pixel resolution of the digital images, and which are composed of spatial coordinates describing the system, each coordinate being associated to a different matrix. The referential transformations can thus be applied by calculating the associated modifications on the matrices, which are then taken as a basis to adapt the image geometric calibration. In order to extensively illustrate this approach, we will use a concrete case of using digital imaging for photometric measurements, where referential variations are present: the bi- directional photogoniometer developed at the Solar Energy and Building Physics Laboratory (LESO-PB, EPFL) for light transmission measurements. Details on its calibration procedures, image and data processing and results can be found in [3].