HW1_sol - CS556 Homework 1 Forrest Briggs 1 Introduction 1...

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CS556: Homework 1 Forrest Briggs January 18, 2010 1 Introduction The goal in this assignment is to write code for: 1. Detecting Harris-afne 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 Harris-afne 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 Multi-scale 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 2d-Gaussian 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 f with a range of values for σ . The values are σ 1 = 2 , σ 2 = 3 , σ
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  • Spring '08
  • Staff
  • Computer vision, Eigenvalue, eigenvector and eigenspace, Blob detection, Interest point detection, Harris Point

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