CS计算机代考程序代写 University at Buffalo

University at Buffalo
Department of Computer Science and and Engineering CSE 473/573 – Computer Vision and Image Processing
Instructions
Spring 2021, TuTh 9:30AM-10:50AM
Homework #5
Due Date: 5/7/21, 11:59PM
• Answer the questions below and provide as much of your work as necessary.
• Export or scan your homework and store it as a PDF version before submitting online to
UBLearns.
1 Camera Calibration (60 points)
The projection from world coordinates to the image plane, can be represented as a combination of intrinsic (camera) parameters and extrinsic (world) parameters. The first step is from the world coordinate (w) to the camera coordinate (c). The extrinsic parameters include one rotation matrix
Xc r11 r12 r13 Xw Tx
and one translation vector: Yc  = r21 r22 r23·Yw +Ty. The second step is from camera
Zc r31r32r33 Zw Tz
xh fx 0 ox Xc coordinate (c) to the image coordinate (i) via intrinsic parameters, yh  =  0 fy oy  ·  Yc .
w 0 0 1 Zc From world coordinates to the camera coordinates, we can incorporate the intrinsic and extrinsic
m11 m12 m13 m14 xh m11 m12 m13 m14 Xw
parameters to get M = m21 m22 m23 m24 , where yh = m21 m22 m23 m24 m31 m32 m33 m34 w m31 m32 m33 m34
·Yw, Zw
  
1 (xi,yi) = (xh/w,yh/w) is the image coordinate, and (Xw,Yw,Zw) is the world coordinate of the corresponding point. Suppose there are N points and the n-th point is indicated by its image
coordinate (xni , yin) and world coordinate (Xwn, Ywn, Zwn).
• Express M using the extrinsic parameters and intrinsic parameters. (10 points)
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CSE 473/573 Homework 5 Spring 2021
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Calculate m231 + m232 + m233. (10 points)
We can build a linear equation: A·m = 0, where A is a 2N ×12 matrix and m = 􏰟m11 m12 m13 m14 … m31 m32 m33 m34􏰠T is a 12 × 1 matrix. Express A only in terms of {xni , yin, Xwn, Ywn, Zwn}, n = 1…N. (20 points)
Since A·x = 0 equals A·(λx) = 0, we have infinite solutions for A·x = 0. Thus weneedtwostepstogetm: 1)SolvexwhereA·x=0and||x||=1;2)Solveλ to get m = λ · x. Suppose we have used single value decomposition (SVD) to get x =
􏰟x11 x12 x13 x14 … x31 x32 x33 x34􏰠T . Express λ and m only in terms of the 12 ele- ments of x. (20 points)
Image Rectification (20 points)
L and R are two images of one object taken from different views. The relationship between the two f11 f12 f13 
image coordinates can be represented by the fundamental matrix F: 􏰟xl yl 1􏰠 · f21 f22 f23 · f31 f32 f33
xr 
yr = 0 , where [xl,yl] and [xr,yr] are the coordinates of the corresponding points on the left and
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right images. We use [xnl , yln] and [xnr , yrn] to denote the left/right coordinate of the n-th point.

We can build a linear system: A · f = 0, where A is a N × 9 matrix and
f = 􏰟f11 f12 f13 f21 f22 f23 f31 f32 of{xnl ,yln,xnr,yrn},n=1…N.
Morphology (20 points)
0 0 0 0 0 0 0 0 0
0 1 1 1 0 0 0 0 0
0 1 1 1 1 0 0 0 0
f33􏰠T is a 9×1 matrix. Express A only in terms
0 0 0 1 1 1 0 0 0
SupposeI=0 0 0 1 1 1 1 0 0,andweconsider3×3squarestructureelement.

0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 000000000
• What is the result applying dilation on I? (10 points) • What is the result applying erosion on I? (10 points)
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