Assume that you are given an image showing the intensity I(x, y) = c exp[-a(x-b)2]. How...
Assume that you are given an image showing the intensity I(x, y) = c exp[-a(x-b)2]. How does the image look like? Can you compute the corresponding Hessian matrix at pixel (x,y)? Does it tell us anything about the image
Homework Answers
Answer:
Given that:
Assume that you are given an image showing the intensity I(x, y) = c exp[-a(x-b)2]. How does the image look like an you compute the corresponding Hessian matrix at pixel (x,y)
Hessian matvix of I (x,y )is given by
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Assume that you are given an image showing the intensity I(x, y)
= c exp[-a(x-b)2]. How...
2. Consider the function f : R2 → R2 given by. (x,y) (a) Compute the Df(x, y) (b) List every vect...
2. Consider the function f : R2 → R2 given by. (x,y) (a) Compute the Df(x, y) (b) List every vector r e R2 such that Df(ri, r2) 0. What can we say about the tangent plane to the surface of the graph at (ri,2,f(r1, r2))? (c) How do you know that the Hessian, Df(x, y) is necessarily symmetric? Recall that t,y D2 f(x,y) , y) (d) What are the eigenva of D2f(r1,r2) for each root of the gradient that...
use MATLAB to upload the following: an image that you want to process (can be taken...
use MATLAB to upload the following:
an image that you want to process (can be taken yourself or
downloaded from the internet)
a script that processes the image in TWO ways.
manipulates the colors
averages pixels together
Please make sure the script displays the images (like how I did
with the 40 and 80 pixel averaging) so I can easily compare them to
the original. Make sure to COMMENT your code as well.
Homework 13 Please upload the following: an...
Q2. Suppose you are given the following Cob-Douglas Production Y; = B1X2 X3 exp(ui) for i...
Q2. Suppose you are given the following Cob-Douglas Production Y; = B1X2 X3 exp(ui) for i = 1, 2, ...,n, where B1, B2 and Bzare population parameters and the Ui are IID (0,02). Note that: Y; routput, X2i =labor input, Xzi =capital input, exp = base of the natural logarithm. (a) Transform the above non-linear model, Yį = B2X2 X : exp(ui) to a linear model (b) How do you the interpret B2? (c) How do you the interpret By?...
WRITE A C++ PROGRAM TO ANSWER THE QUESTIONS BELOW. You are provided with an image in...
WRITE A C++ PROGRAM TO ANSWER THE QUESTIONS BELOW. You are provided with an image in a new file format called JBC Here is an example of the format: 2 3 100 50 40 200 66 56 12 45 65 23 67 210 0 255 100 45 32 123 The first line means that this is a 2 (width) by 3 (height) image of pixels. Then, each line represents the color of a pixel. The numbers are from 0 to...
Problem 2.2 n and let X ε Rnxp be a full-rank matrix, and Assume p Note that H is a square n × n ...
Please show all work in READ-ABLE way. Thank you so much in
advance.
Problem 2.2 n and let X ε Rnxp be a full-rank matrix, and Assume p Note that H is a square n × n matrix. This problem is devoted to understanding the properties H Any matrix that satisfies conditions in (a) is an orthogonal projection matriz. In this problem, we will verify this directly for the H given in (1). Let V - Im(X). (b) Show that...
A discrete-time system has a difference equation given by y(n) = y(n-1) - 2y(n-2) + x(n) + 2x(n-1) + x(n-2)
A discrete-time system has a difference equation given by y(n) = y(n-1) - 2y(n-2) + x(n) + 2x(n-1) + x(n-2). (a) Find h(n) using iteration. (b) Find the system's z-transfer function H(z). (c) Assume x(n) = δ(n) - 2δ(n-1) + 3δ(n-2). Find y(3) using any method you like. (d) Is this system a FIR or IRR system? How can you tell?
Given the following model: Y= C + I + G + X – Z C =...
Given the following model: Y= C + I + G + X – Z C = a + bYd Z = Z0 + zYd Yd = Y – T a) Compute the expression for equilibrium income b) Compute the expression for the tax multiplier c) Suppose there is an autonomous increase in imports (Z0) of 20 units. To counteract this contraction in domestic aggregate demand, assume the government cuts taxes by 20 units. Will equilibrium income rise or fall? By...
Given the following model: Y= C + I + G + X – Z C =...
Given the following model: Y= C + I + G + X – Z C = a + bYd Z = Z0 + zYd Yd = Y – T a) Compute the expression for equilibrium income b) Compute the expression for the tax multiplier c) Suppose there is an autonomous increase in imports (Z0) of 20 units. To counteract this contraction in domestic aggregate demand, assume the government cuts taxes by 20 units. Will equilibrium income rise or fall? By...
2. Consider a simple linear regression i ion model for a response variable Y, a single...
2. Consider a simple linear regression i ion model for a response variable Y, a single predictor variable ,i1.., n, and having Gaussian (i.e. normally distributed) errors: This model is often called "regression through the origin" since E(X) = 0 if xi = 0 (a) Write down the likelihood function for the parameters β and σ2 (b) Find the MLEs for β and σ2, explicitly showing that they are unique maximizers of the likelihood function Hint: The function g(x)log(x) +1-x...
If the values of the joint distribution of two continuous random variables X and Y is given by: f(x, y) = (x+y)/3 for 0 < x < 1 and 0 < y < 2 0 otherwise
(a) fX(x)
(b) fY (y)
(c) f(x|y = 1)
(d) E(X)
(e) E(X2
)
(f) V ar(X)
(g) E(X|y = 1)
(h) What can you tell about E(X) and E(X|y = 1)?Are they different?
If so, which one is higher? What is the intuition behind this result?
(i) E(X2
|y = 1)
(j) V ar(X|y = 1)
(k) What can you tell about V ar(X) and V ar(X|y = 1)? Are they
different? If so, which one is higher? What...
2. Consider the function f : R2 → R2 given by. (x,y) (a) Compute the Df(x, y) (b) List every vector r e R2 such that Df(ri, r2) 0. What can we say about the tangent plane to the surface of the graph at (ri,2,f(r1, r2))? (c) How do you know that the Hessian, Df(x, y) is necessarily symmetric? Recall that t,y D2 f(x,y) , y) (d) What are the eigenva of D2f(r1,r2) for each root of the gradient that...
use MATLAB to upload the following:
an image that you want to process (can be taken yourself or
downloaded from the internet)
a script that processes the image in TWO ways.
manipulates the colors
averages pixels together
Please make sure the script displays the images (like how I did
with the 40 and 80 pixel averaging) so I can easily compare them to
the original. Make sure to COMMENT your code as well.
Homework 13 Please upload the following: an...
Q2. Suppose you are given the following Cob-Douglas Production Y; = B1X2 X3 exp(ui) for i = 1, 2, ...,n, where B1, B2 and Bzare population parameters and the Ui are IID (0,02). Note that: Y; routput, X2i =labor input, Xzi =capital input, exp = base of the natural logarithm. (a) Transform the above non-linear model, Yį = B2X2 X : exp(ui) to a linear model (b) How do you the interpret B2? (c) How do you the interpret By?...
Please show all work in READ-ABLE way. Thank you so much in
advance.
Problem 2.2 n and let X ε Rnxp be a full-rank matrix, and Assume p Note that H is a square n × n matrix. This problem is devoted to understanding the properties H Any matrix that satisfies conditions in (a) is an orthogonal projection matriz. In this problem, we will verify this directly for the H given in (1). Let V - Im(X). (b) Show that...
2. Consider a simple linear regression i ion model for a response variable Y, a single predictor variable ,i1.., n, and having Gaussian (i.e. normally distributed) errors: This model is often called "regression through the origin" since E(X) = 0 if xi = 0 (a) Write down the likelihood function for the parameters β and σ2 (b) Find the MLEs for β and σ2, explicitly showing that they are unique maximizers of the likelihood function Hint: The function g(x)log(x) +1-x...
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