assignment 2 - Page 1 of 4 CS 359 Medical Image...

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Page 1 of 4 CS 359 Medical Image Registration J. M. Fitzpatrick Assignment 2, Due Thursday, Oct 6. Problem 1 This is a problem to turn in on paper only. It is a set of short derivations from class. We were discussing point-based rigid registration, where the set of points { } i x were to be registered to the set { } i y . a) Define 2 1 N i i i G Rx t y = = + - . Show that, if x and y are the mean values, respectively, of the two sets of points, then 2 2 1 2 3 1 2 ( ) N i i i G a t a t Rx y a Rx y = = + - + - . Give the values of 1 a , 2 a , and 3 a . b) Show that 2 2 2 1 2 3 1 ( ) . N i i i G b t y Rx b Rx y b Rx y = = - - + - + - Give the values of 1 b , 2 b , and 3 b . c) Show that, if t has been given the value that minimizes G , and if i x % and i y % are the demeaned point positions, 2 1 1 N i i i G c Rx y = = - % % . Give the value of 1 c . d) Show that, if X and Y are the3 N × point matrices, as defined in class (each column contains one point vector), then 1 trace(( ) ), N t i i i Rx y RX Y = = % % e) Show that trace( ) trace( ) t A A = (Too easy, just here for completeness!) f) Show that trace( ) trace( ) AB BA = . g) Using (e) and (f) show that trace(( ) ) trace( ) t RX Y RH = , where t H XY = . h) Show that if Λ is a diagonal matrix, then trace( ) ii ii i Z Z Λ = Λ .
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Page 2 of 4 Problem 2 For this problem you are to write the following Matlab functions:
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This note was uploaded on 01/10/2010 for the course ECE 291 specia taught by Professor Prof.fitzpatrick during the Fall '05 term at Vanderbilt.

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assignment 2 - Page 1 of 4 CS 359 Medical Image...

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