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Disc: Approximative Nearest Neighbor Search using Ellipsoids for Photon Mapping on GPUs
KTH, School of Computer Science and Communication (CSC).
KTH, School of Computer Science and Communication (CSC).
2016 (English)Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesisAlternative title
Disc : Approximativ närmaste grannsökning med ellipsoider för fotonmappning på GPU:er (Swedish)
Abstract [en]

Recent development in Graphics Processing Units (GPUs) has enabled inexpensive high-performance computing for general-purpose applications. The K-Nearest Neighbors problem is widely used in applications ranging from classification to gathering of photons in the Photon Mapping algorithm. Using the euclidean distance measure when gathering photons can cause false bleeding of colors between surfaces. Ellipsoidical search boundaries for photon gathering are shown to reduce artifacts due to this false bleeding. Shifted Sorting has been found to yield high performance on GPUs while simultaneously retaining a high approximation rate. This study presents an algorithm for approximatively solving the K-Nearest Neighbors problem modified to use a distance measure creating an ellipsoidical search boundary. The ellipsoidical search boundary is used to alleviate the issue of false bleeding of colors between surfaces in Photon Mapping. The Approximative K-Nearest Neighbors algorithm presented is a modification of the Shifted Sorting algorithm. The algorithm is found to be highly parallelizable and performs to a factor of 86% queries processed per millisecond compared to a reference implementation using spherical search boundaries implied by the euclidean distance. The rate of compression from spherical to ellipsoidical search boundary is appropriately chosen in the range 3.0 to 7.0. The algorithm is found to scale well in respect to increases in both number of data points and number of query points.

Abstract [sv]

Grafikprocessorer (GPU-er) har på senare tid möjliggjort högprestandaberäkningar till låga kostnader för generella applikationer. K-Nearest Neighbors problemet har vida applikationsområden, från klassifikation inom maskininlärning till insamlande av fotoner i Photon Mapping för rendering av tredimensionella scener. Användning av euklidiska avstånd vid insamling av fotoner kan leda till en felaktig bladning av färger mellan ytor. Ellipsoidiska sökområden vid fotoninsamling har visats reducera artefakter oraskade av denna typ av felaktiga färgutblandning. Shifted Sorting har visats ge hög prestanda på GPU-er utan att förlora kvalitet av approximationsgrad. Denna rapport undersöker hur den approximativa varianten av K-Nearest Neighborsalgoritmen med Shifted Sorting presterar på GPU-er med avståndsmåttet modifierat sådant att ett ellipsoidiskt sökområde bildas. Algoritmen används för att reduceras problemet av felaktig blanding av färg i Photon Mapping. Algoritmen visas vara mycket parallelliserbar och presterar till en grad av 86% behandlade sökpunkter per millisekund i jämförelse med en referensimplementation som använder sfäriska sökområden. Kompressionsgraden längs sökpunktens ytnormal väljs fördelaktligen till ett värde i intervallet 3,0 till 7,0. Algoritmen visas skala väl med avseende på både ökningar i antal data punkter och antal sökpunkter.

Place, publisher, year, edition, pages
2016. , 44 p.
Keyword [en]
photon mapping, k-nearest neighbors, ellipsoid, gpu, parallel
National Category
Computer Science
Identifiers
URN: urn:nbn:se:kth:diva-186502OAI: oai:DiVA.org:kth-186502DiVA: diva2:927475
Educational program
Master of Science in Engineering - Computer Science and Technology
Supervisors
Examiners
Available from: 2016-05-12 Created: 2016-05-12 Last updated: 2016-05-12Bibliographically approved

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