Incremental Voxel Colouring by Ray Traversal O. Batchelor, R. Mukundan, R. Green University of Canterbury, Dept. Computer Science& Software Engineering. owb13@student.canterbury.ac.nz, {Mukundan, Richard.Green}@canterbury.ac.nz Abstract Image based reconstruction from multiple views is an interesting challenge. Recently methods of optimisation based voxel colouring have appeared, which make use of incremental visibility updates. We present an alternative incremental voxel colouring algorithm in the mould of GVC-LDI [2] which directly as- sociates each visible voxel with the set of rays in it’s visible projection, using ray-voxel traversal as a mechanism for updates. We make some time comparisons using calibrated pho- tographs and synthetic images, as well looking at optimi- sation based voxel colouring and level of detail. Results show that our method compares favourably to GVC-LDI. Keywords— Voxel Colouring, Ray Tracing, Reconstruc- tion, Computer Vision 1 Introduction We introduce a derivative method of using ray traver- sal for determining visibility incrementally. Like Voxel Colouring [6], Space Carving [4] and GVC-LDI [2], the algorithm works on reconstructing a volumetric scene us- ing colour consistency primarily. Unlike earlier works, we have looked at using ray traversal as the primary method of updating visibility. Our algorithm works on an arbitrary collection of rays rather than a set of images. Though we convert calibrated images to a set of rays for input. Our primary reasons for looking into ray traversal are the potential of optimisation colour consistency and benefits associated with incremental visi- bility – fast convergence and flexible carving order. Due to the nature of the problem we refer to rays and pixels interchangeably, where a ray can be generated from the inverse projection (of the calibrated image’s projection matrix). 2 Background Voxel Colouring [6] and derivatives are methods for re- constructing a scene from a set of calibrated images. A scene is represented by voxels, which are defined to be a unit of volume, in our case a cube. The primary character- istics of voxel colouring are it’s explicit handling of visibil- ity and it’s local decision function for opaqueness, colour consistency. Space carving [4] introduced the idea of conservative carving and defined the photo hull. This entails progres- sively carving from an estimate of the true scene, while using the estimate as an approximation for visibility. The space carving algorithm performs reconstruction with ar- bitrary view configurations by using a plane sweep method where a mask is used in each image to mark occlusion. 2.1 Generalised Voxel Colouring Generalised Voxel Colouring [2] built on this idea, ex- tending it to support full use of all scene views symmetri- cally, with arbitrary view placement. The key data struc- ture used by GVC is an item buffer which stores the closest visible voxel for every pixel in an image (shown in 1). The second (GVC-LDI) uses layered depth images of surface voxels as item buffers, as the voxel model is up- dated the layered depth images are updated incrementally. A LDI consists of surface voxel intersections, shown in fig- ure 1). The basic GVC algorithm performs updates in par- allel across surface (SVL) voxels, and suffers from re- calculation as the algorithm becomes close to converging, where as GVC-LDI is a serial process. 2.2 Reprojection error A useful measure for evaluating the results of recon- structions, as well as a measure of colour consistency is the reprojection error. Where the output image of voxels are reprojected and the difference taken with input images on a pixel by pixel basis. A common distance used is the square of differences per component, equation 1, where C1 α cor- respond to a colour component, α = {r, g, b} for a RGB image. dist(C1,C2) =  α=1 (C1 α - C2 α ) 2 (1)