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Consider a natural number N = p. q where p, q are large prime numbers. Construct a set `y ` is called a Quadratic Residue (QR), if x | y = x 2 and x, y else ` y ` is called a Quadratic Non-Residue (QNR). Construct a set Y N with equal number of QRs and QNRs. Root Info.
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Consider a natural number N = p. q where p, q are large prime numbers. • Construct a set • `y` is called a Quadratic Residue (QR), if x | y = x2 and x, y else `y` is called a Quadratic Non-Residue (QNR). • Construct a set YN with equal number of QRs and QNRs Root Info Feature vector (fquery) Q1 fquery, f(A1) A1 Q2 …….. fquery, f(A2) A2 ….. ….. 0 1 1 QR 0 1 1 ….. ….. 1 0 1 QNR 1 0 1 …. …. …. …. …. …. …. ….. ….. 1 0 1 QR 1 0 1 m x n m x n ….. ….. QR QR2 QR2 QR QR2 QR2 ….. ….. QNR2 QNR QNR2 QNR2 QNR QNR2 …. …. …. …. …. …. ….. ….. QR2 QR QR2 QR2 QR QR2 ….. Ai QR QNR QR Private Content Based Image Retrieval Shashank J, Kowshik P, Kannan Srinathan and C.V. Jawahar Is it possible for an image database to respond accurately without any knowledge of the query image. • Objective: • Retrieve results from an image database, while maintaining complete privacy of the query image from the database. • Applications:: • Medical Image Databases • Surveillance Systems • Logo Patent Search • Defense Systems • Web 2.0 • Image based query retrieval Extension to other Hierarchical Structures Results and Discussions Quadratic Residuosity Assumption • KD Tree and Corel Dataset • Color Histogram (768 dimensions) • Retrieval Time: 0.596 secs • Vocabulary Tree and Nister Dataset • SIFT features • Vocabulary of 10000 visual words. • Retrieval Time: 0.320 secs • LSH and Corel Database • Used to achieve partial privacy. • 90 Hash functions with 450 bins each. • Retrieval Time: 0.221 secs • Related Work • Blind Vision by S. Avidan and M. Butman • Apply secure multi-party techniques to vision algorithms. • Multi-party protocols are inefficient compared to our tailor made solution. • They need privacy in both directions while PCBIR demands in one direction only. • Hierarchical Structures vary in: • Number of nodes at each level. • Information at a node. • Any number of nodes can be converted into a ‘m x n’ matrix. • Any information can be represented in binary format. • If the user has the data about the indexing structure and the format of the information stored at a node, the algorithm can be simulated for any hierarchical structure. • KD Tree • Similar to binary tree • Each node contains split dimension and split value. • Vocabulary Tree • Branch factor depends on vocabulary size. • Each node contains representative visual words of its children. Quadratic Residuosity Assumption: Given a number `y` YN, it is predictably hard to decide whether `y` is a QR or a QNR. Basic Properties: QNR x QNR = QR QNR x QR = QNR QR x QR = QR PCBIR Algorithm Extract feature vector of the query image say fquery. The user first asks the database to send the information at the root node. Using fquery and the information received, the user decides whether to access the left subtree or the right subtree. In order to get the data at the node to be accessed, the user frames a query Qi where i indicates the level in which the node occurs. The database returns a reply Ai for the query Qi. The user using the data obtained from Ai and fquery decides which subtree to move next to. PCBIR on a Binary Search Tree Formulation of Qi and Ai Center for Visual Information Technology International Institute of Information Technology, Hyderabad, INDIA http://cvit.iiit.ac.in
