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Princeton COS 598B - LDI Tree: A Hierarchical Representation

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ABSTRACTINTRODUCTIONRELATED WORKInverse WarpingLayered Depth ImageVolumetric MethodsImage Caching for Rendering Polygonal ModelsLDI TREEConstructing the LDI Tree from Multiple Reference ImagesRendering the Output ImagesCompositing in the Output BufferProgressive RefinementGap FillingAnalysis of Memory RequirementRendering TimeRESULTSCONCLUSION AND FUTURE WORKACKNOWLEDGEMENTSREFERENCESLDI Tree: A Hierarchical Representation for Image-Based RenderingChun-Fa Chang Gary Bishop Anselmo LastraUniversity of North Carolina at Chapel HillABSTRACTUsing multiple reference images in 3D image warping has been achallenging problem. Recently, the Layered Depth Image (LDI)was proposed by Shade et al. to merge multiple reference imagesunder a single center of projection, while maintaining the simplic-ity of warping a single reference image. However it does notconsider the issue of sampling rate.We present the LDI tree, which combines a hierarchical spacepartitioning scheme with the concept of the LDI. It preserves thesampling rates of the reference images by adaptively selecting anLDI in the LDI tree for each pixel. While rendering from the LDItree, we only have to traverse the LDI tree to the levels that arecomparable to the sampling rate of the output image. We alsopresent a progressive refinement feature and a “gap filling” algo-rithm implemented by pre-filtering the LDI tree.We show that the amount of memory required has the sameorder of growth as the 2D reference images. This also bounds thecomplexity of rendering time to be less than directly renderingfrom all reference images.CR Categories: I.3.3 [Computer Graphics]: Picture/Image Gen-eration - Viewing Algorithms; I.3.6 [Computer Graphics] Meth-odology and Techniques - Graphics data structures and data types;I.3.7 [Computer Graphics]: Three-Dimensional Graphics andRealism.Additional Keywords: image-based rendering, hierarchical rep-resentation1. INTRODUCTIONThe 3D Image warping algorithm [14] proposed by McMillan andBishop uses regular single-layered depth images (which are calledreference images) as the initial input. One of the major problemsof 3D image warping is the disocclusion artifacts which arecaused by the areas that are occluded in the original referenceimage but visible in the current view. Those artifacts appear astears or gaps in the output image. In Mark’s Post-RenderingWarping [11], the techniques of splatting and meshing are pro-posed to deal with the disocclusion artifacts. Both splatting andmeshing are adequate for post-rendering warping in which thecurrent view does not deviate much from the view of the referenceimage.However, the fundamental problem of the disocclusion arti-facts is that the information of the previously occluded area ismissing in the reference image. By using multiple reference im-ages taken from different viewpoints, the disocclusion artifactscan be reduced because an area that is not visible from one viewmay be visible from another. When multiple source images areavailable, we expect the disocclusion artifacts that occur whilewarping one reference image to be eliminated by one of the otherreference images. However, combining multiple reference imagesand eliminating the redundant information is a non-trivial prob-lem, as pointed out by McMillan in his discussion of inversewarping [15].Recently, the Layered Depth Image (LDI) was proposed byShade et al. [19] to merge many reference images under a singlecenter of projection. It tackles the occlusion problems by keepingmultiple depth pixels per pixel location, while still maintaining thesimplicity of warping a single reference image. Its limitation isthat the fixed resolution of the LDI may not provide an adequatesampling rate for every reference image. Figure 1 shows twoexamples of such situations. Assuming the two reference imageshave the same resolution as the LDI, the object covers more pixelsin reference image 1 than it does in the LDI. Therefore the LDIhas a lower sampling rate for the object than reference image 1.Similar analysis shows the LDI has a higher sampling rate thanreference image 2. If we combine both reference images into theLDI and render the object from the center of projection of refer-ence image 1, the insufficient sampling rate of the LDI will causethe object to look more blurry than it looks in reference image 1.When we render the object from the center of projection of refer-ence image 2, the excessive sampling rate of the LDI might nothurt the quality of the output. However, processing more pixelsthan necessary slows down the rendering.In this paper, we present the LDI Tree, which combines a hi-erarchical space partition scheme with the concept of the LDI. Itpreserves the sampling rate of the reference images by adaptivelyselecting an LDI in the LDI tree for each pixel. While renderingfrom the LDI tree, we only have to traverse the LDI tree to thelevels that are comparable to the sampling rate of the output im-age. Because each LDI also contains pre-filtered results from itschildren LDIs, progressive refinement is easy to implement. Thepre-filtering also enables a new “gap filling” algorithm to fill thedisocclusion artifacts that cannot be resolved by any referenceimage.The amount of memory required has the same order of growthas the 2D reference images. Therefore the LDI tree preserves animportant feature that image-based rendering has over traditionalpolygon-based rendering: the cost is bounded by the complexityof the reference images, not by the complexity of the scene.2. RELATED WORK2.1. Inverse WarpingThe image warping described in [14] is a forward warping proc-ess. The pixels of the reference images are traversed and warpedto the output image in the order they appear in the reference im-ages. Some pixels in the output image may receive more thanCB#3175 Sitterson Hall, Chapel Hill, NC 27599-3175, USA.{chang, gb, lastra}@cs.unc.edu http://www.cs.unc.edu/~ibrPermission to make digital or hard copies of all or part of this work forpersonal or classroom use is granted without fee provided that copiesare not made or distributed for profit or commercial advantage and thatcopies bear this notice and the full citation on the first page. To copyotherwise, to republish, to post on servers or to redistribute to lists,requires prior specific permission and/or a fee.SIGGRAPH 99, Los Angeles, CA USACopyright ACM 1999 0-201-48560-5/99/08 . . . $5.00291one warped pixel and some may receive none,


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Princeton COS 598B - LDI Tree: A Hierarchical Representation

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