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Unformatted text preview: CS556: Homework 1 Forrest Briggs January 18, 2010 1 Introduction The goal in this assignment is to write code for: 1. Detecting Harrisafne corners in an image, by (a) Detecting multiscale Harris points, (b) Automatically selecting the scale of each detection, (c) Fitting an ellipse to each image region occupied by a Harris corner, 2. Computing their rotation and scale invariant DAISY descriptors, based on the ellipses identied in the previous step, 3. Matching Harrisafne corners detected in two images showing the same scene, by nding for each point in image 1 another point in image 2 with the smallest Euclidean distance of their associated rotation and scale invariant DAISY descriptors. 2 Literature Review Moravec proposed a simple corner detector for robotic vision [1]. The idea is to measure the different between the image in a small window centered around a candidate point and a window shifted in each of the 8 neighboring directions. This detector would be very fast to compute, but it is not rotation invariant. Tomasi et. al. [3] propose a variation on the Harris detector which uses the same matrix M (see the following section), but rather than computing f σ ( x,y ) = det ( M σ ( x,y )) trace ( M σ ( x,y )) , they instead use f σ ( x,y ) = min ( λ 1 ,λ 2 ), i.e. the minimum of the two eigenvalues of M . They argue that this is a better corner detection function when affine transformations are present. This method would be slower than Harris corners however, because it requires calculating eigenvalues. 3 Description of Methods This section describes the Harris interest point detection and DAISY descriptors. 3.1 Detecting Multiscale Harris Points We begin with an m x n image I ( x,y ). At each pixel ( x,y ) we must compute a matrix H , defined as: M σ ( x,y ) = G ( x,y,σ ) * I 2 x I x I y I x I y I 2 y G is the 2dGaussian kernel, G ( x,y,σ ) = 1 2 πσ 2 e ( x 2 + y 2 ) / 2 σ 2 , and I x and I y are the spatial derivatives of I . Then we compute f σ ( x,y ) = det ( M σ ( x,y )) trace ( M σ ( x,y )) . To make the interest point detection process scale invariant, we evaluate....
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This note was uploaded on 04/17/2010 for the course CS 261 taught by Professor Staff during the Spring '08 term at Oregon State.
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