CS-184: Computer GraphicsLecture #7: Raytracing Prof. James O’BrienUniversity of California, BerkeleyV2006-F-07-1.02TodayRaytracingShadows and direct lightingReflection and refractionAntialiasing, motion blur, soft shadows, and depth of fieldIntersection TestsRay-primitiveSub-linear tests3Light in an EnvironmentLady writing a Letter with her Maid National Gallery of Ireland, DublinJohannes Vermeer, 16704Global Illumination EffectsPCKTWTCHKevin OdhnerPOV-Ray5Global Illumination EffectsA Philco 6Z4 Vacuum TubeSteve AngerPOV-Ray6Global Illumination EffectsCaustic SphereHenrik Jensen(refraction caustic)7Global Illumination EffectsCaustic RingHenrik Jensen(reflection caustic) 8Global Illumination EffectsSphere FlakeHenrik Jensen9Early RaytracingTurner Whitted10RaytracingScan conversion3D ! 2D ! ImageBased on transforming geometryRaytracing3D ! ImageGeometric reasoning about light rays11RaytracingEye, view plane section, and scene12RaytracingLaunch ray from eye through pixel, see what it hits13RaytracingCompute color and fill-in the pixel14RaytracingBasic tasksBuild a rayFigure out what a ray hitsCompute shading15Building Eye RaysRectilinear image plane build from four pointsLLLRURULEPuvP = u (vLL + (1 − v)UL)+(1 − u)(vLR + (1 − v)UR)16Building Eye RaysNonlinear projectionsNon-planar projection surfaceVariable eye location17ExamplesMultiple-Center-of-Projection ImagesPaul Rademacher Gary BishopUniversity of North Carolina at Chapel HillABSTRACTIn image-based rendering, images acquired from a scene areused to represent the scene itself. A number of reference imagesare required to fully represent even the simplest scene. This leadsto a number of problems during image acquisition and subsequentreconstruction. We present the multiple-center-of-projectionimage, a single image acquired from multiple locations, whichsolves many of the problems of working with multiple rangeimages.This work develops and discusses multiple-center-of-projection images, and explains their advantages overconventional range images for image-based rendering. Thecontributions include greater flexibility during image acquisitionand improved image reconstruction due to greater connectivityinformation. We discuss the acquisition and rendering ofmultiple-center-of-projection datasets, and the associatedsampling issues. We also discuss the unique epipolar andcorrespondence properties of this class of image.CR Categories: I.3.3 [Computer Graphics]: Picture/Image Generation –Digitizing and scanning, Viewing algorithms; I.3.7 [Computer Graphics]:Three-Dimensional Graphics and Realism; I.4.10 [Image Processing]:Scene AnalysisKeywords: image-based rendering, multiple-center-of-projection images1 INTRODUCTIONIn recent years, image-based rendering (IBR) has emergedas a powerful alternative to geometry-based representations of3-D scenes. Instead of geometric primitives, the dataset in IBR isa collection of samples along viewing rays from discretelocations. Image-based methods have several advantages. Theyprovide an alternative to laborious, error-prone geometricmodeling. They can produce very realistic images when acquiredfrom the real world, and can improve image quality whencombined with geometry (e.g., texture mapping). Furthermore,the rendering time for an image-based dataset is dependent on theimage sampling density, rather than the underlying spatialcomplexity of the scene. This can yield significant renderingspeedups by replacing or augmenting traditional geometricmethods [7][23][26][4].The number and quality of viewing samples limits thequality of images reconstructed from an image-based dataset.Clearly, if we sample from every possible viewing position andalong every possible viewing direction (thus sampling the entireplenoptic function [19][1]), then any view of the scene can bereconstructed perfectly. In practice, however, it is impossible tostore or even acquire the complete plenoptic function, and so onemust sample from a finite number of discrete viewing locations,thereby building a set of reference images. To synthesize animage from a new viewpoint, one must use data from multiplereference images. However, combining information fromdifferent images poses a number of difficulties that may decreaseboth image quality and representation efficiency. The multiple-center-of-projection (MCOP) image approaches these problemsby combining samples from multiple viewpoints into a singleimage, which becomes the complete dataset. Figure 1 is anexample MCOP image.Figure 1 Example MCOP image of an elephantThe formal definition of multiple-center-of-projectionimages encompasses a wide range of camera configurations. Thispaper mainly focuses on one particular instance, based on thephotographic strip camera [9]. This is a camera with a verticalslit directly in front of a moving strip of film (shown in Figure 2without the lens system). As the film slides past the slit acontinuous image-slice of the scene is acquired. If the camera ismoved through space while the film rolls by, then differentcolumns along the film are acquired from different vantage points.This allows the single image to capture continuous informationfrom multiple viewpoints. The strip camera has been usedextensively, e.g., in aerial photography. In this work’s notion of adigital strip camera, each pixel-wide column of the image isacquired from a different center-of-projection. This single imagebecomes the complete dataset for IBR.Features of multiple-center-of-projection images include:• greater connectivity information compared withcollections of standard range images, resulting inimproved rendering quality,• greater flexibility in the acquisition of image-baseddatasets, for example by sampling different portions ofthe scene at different resolutions, and• a unique internal epipolar geometry whichcharacterizes optical flow within a single image.!!!!!!!!!!! CB #3175 Sitterson Hall, Chapel Hill, NC, 27599-3175 [email protected], [email protected] http://www.cs.unc.edu/~ibrMultiple-Center-of-Projection ImagesP. Rademacher and G. BishopSIGGRAPH
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