CS 563 Advanced Topics in Computer Graphics View
- Slides: 26
CS 563 Advanced Topics in Computer Graphics View Interpolation and Image Warping by Brad Goodwin Images in this presentation are used WITHOUT permission
Over View § General Imaged-Based Rendering § Interpolation § Plenoptic Function § Layered Depth Image (LDI)
Introduction § Image Based Rendering (IBR) § § § § Composed of photometric observations Mix of fields (photogrammetry, vision, graphics) Texture mapping Environment mapping Realistic surface models Uses from virtual reality to video games Just render the 3 D scene? Judge results? § Different types of rendering using different amounts of geometry
Interpolation § Morphing § interpolating texture map and shape § Generation of a new image is independent of scene complexity § Morph adjacent images to view between § based on viewpoints being closely spaced § Uses camera position, orientation and range to deteremine pixel by pixel § Images pre computed and stored as morph maps
About this method § Method can be applied to natural images § Only synthetic were tested with this paper § Of course this paper was in ’ 93 so hopefully someone’s tested them by now § Only accurately supports view independent shading § Others could be used on maps but they are discussed
Types of Images § Can be done with natural or sythetic images § Sythetic § easy to get the range and camera data § Natural § Use ranging camera § Computed by photogrammetry or artist
General Setup § Morphing can interpolate different parameters § § Camera position Viewing angle Direction of view Hierarchical object transformation § Find correspondence of images § Images arranged in graph structure
Find correspondence § Usually done by animator § This method § Form of forward mapping § uses camera and range to do it § Cross dissolving pixels(not view-independent) § Done for each source image § Quadtree compression § Move groups of pixels § Scene moves opposite camera § Offset vectors for each pixel (“morph map”) § Small change more accurate when interpolated
§ Sampled every 20 pixels Offset vectors
Overlaps and holes § Overlaps § Local image contraction - several samples move to the same pixel in interpolated image § Perpendicular to oblique § Holes § Show when mapping source to destination § Background color § Interpolate four corners of the pixel instead of center (filling and filtering) § Interpolate adjacent offset vectors § Or if part seen in interpolated but not source
Block Compression § Pixels ten to move together so block compression algorithm is used to compress morph map. § Related to image depth complexity § High complexity low compression ratio
View independent Priority § Established to determine points that are viewable § Pixels are ordered from back to front based on Zcoordinates established in morph map § Eliminates need for interpolating the Z-coordinates of every pixel and updating the Z-buffer in the interpolation process.
Applications § Virtual Reality § Motion blur § Uses super-sampling of many images computationally which is expensive thus inefficient § Reduce cost of computing a shadow map § Only for point light sources § Create 3 D primitives without creating 3 D primitives
Plenoptic Modeling § The Plenoptic function § Latin root plenus – complete or full optic - pertaining to vision § Parameterized function for describing everything that is visible from a given point in space § Used as a taxonomy to evaluate low-level vision § Adelson and Bergen postulate “…all the basic visual measurements can be considered to characterize local change along one or tow dimensions of a single function that describes the sructure of the information in the light impinging on an observer. ”
Parameters § azimuth and elevation angle
Plenoptic § Set of all possible environment maps for a given scene § Specify point and range for some constant t § A complete sample can be defined as a full spherical map
Plenoptic Modeling § Claimed that all image-based rendering approaches are just attempts to create a plenoptic function with just a sampling of it § Set up is the same as most approaches § Set of reference images which are warped to create instances of the scene from arbitrary view points
Sample Representation § Unit sphere § Hard to store on a computer § Example of all distorted maps § Six planar projections of a cube § Easy to store § 90 degree face requires expensive lens system to avoid distortion § Oversampling in corners § Have to choose Cylindrical § Easily unrolled § Finite height : problems with boundary conditions § No end caps
Aquiring Cylindrical Projections § Get the projections is simple § Tripod that can continuously pan § Ideally camera’s panning motion should be exact center of tripod § When panning objects are far away slight misalignment is tolerated § Panning takes place entirely on the x-z plane § Both images should have points within each other.
§ Find the projection of the output camera on input cameras image plane § That is the intersection of the line joining the two camera locations with the input camera’s image plane § Line joining the two cameras is the epipolar line § Intersection with the image plane is the epipolar point
§ Map image point to output cylinder § Same techique for comparing points used with face mapping from last week
Layered Depth Images § Paper presents some methods to render multiple frames per second on a PC § Sprites – are texture maps or images with alphas (transparent pixels) rendered onto planar surfaces § One method warps Sprits with Depth § Warps depth values and uses this information to add parallax correction to a standard sprite renderer § LDI § Single input camera § Contains multiple pixels along each line of sight § Size of representation grows linearly with the depth complexity of the scene § Uses Mc. Millan’s warp odering algorithm because data is represented in a single image coordinate system.
References § § § § Chen S E and Williams L, "View Interpolation for Image Synthesis", Proc. ACM SIGGRAPH '93 Mc. Millan L, and Bishop, "Plenoptic Modeling: An Image-based Rendering System", Proc. ACM SIGGRAPH '95 Shade, Gortler, He and Szeliski, "Layered-Depth Images", Proc. ACM SIGGRAPH '98 Mc. Millan L. and Gortler S, "Applications of Computer Vision to Computer Graphics: Image-Based Rendering - A New Interface Between Computer Vision and Computer Graphics, ACM SIGGRAPH Computer Graphics Newsletter, vol 33, No. 4, November 1999 Shum, Heung-Yeung and Kang, Sing Bing, A Review of Imagebased Rendering Techniques, Microsoft Research Watt, 3 D Graphics 2000, Image-based rendering and phtomodeling (Ch 16) http: //www. widearea. co. uk/designer/anti. html http: //www. dai. ed. ac. uk/CVonline/LOCAL_COPIES/EPSRC_SSAZ/n ode 18. html http: //www. cs. northwestern. edu/~watsonb/school/teaching/395. 2 /presentations/14
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