# (“Screened Poisson smoothing”) Suppose we sample a function f(x) at n positions x 1 , x 2 , . . . , x n , yielding a point  ≡ (f(x 1 ), f(x 2 ), . . . , f(x n )) ∈ R n . Our measurements might be...

(“Screened Poisson smoothing”) Suppose we sample a function f(x) at n positions x1, x2, . . . , xn, yielding a point
≡ (f(x1), f(x2), . . . , f(xn)) ∈ R
n. Our measurements might be noisy, however, so a common task in graphics and statistics is to smooth these values to obtain a new vector
∈ R
n.

(a) Provide least-squares energy terms measuring the following: (i) The similarity of
and
. (ii) The smoothness of
. Hint: We expect f(xi+1) − f(xi) to be small for smooth f.

(b) Propose an optimization problem for
using the terms above to obtain
, and argue that it can be solved using linear techniques.

(c) Suppose n is very large. What properties of the matrix in 4.13b might be relevant in choosing an effective algorithm to solve the linear system?

Answered 144 days AfterMay 13, 2022

## Answer To: (“Screened Poisson smoothing”) Suppose we sample a function f(x) at n positions x 1 , x 2 , . . . ,...

Banasree answered on Oct 04 2022
(“Screened Poisson smoothing”) Suppose we sample a function f(x) at n positions x1, x2, . . . , xn, yielding a point  ≡ (f(x1), f(x2), . . . , f(xn)) ∈ R n. Our measurements might be noisy, however, so a common task in graphics and statistics is to smooth these values to obtain a new vector  ∈...
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