University:
Massachusetts Institute of Technology
Course:
6.801 | Machine Vision
Academic year:

2019
Views:

384

Pages:

5
Author:

Raina Ballard

6.866 Quiz #1 Oct. 19 Quiz #2 Nov. 30 Yajun Fang (6) Estimating motion As example, A vector (x,y), 1 variable E = brightness = x = position on the image [Diagram: A sine wave is shown with E on the y-axis and x on the x-axis. Arrows indicate the direction of increasing x and E.] u = velocity = ∂x/∂t u.E_x + E_t = 0. [Diagram: A zoomed-in section of the sine wave is shown with a tangent line drawn at a point.] E_x = (E_i+1 - E_i)/δx and E_t = (E_i+1 - E_i)/δt or: u = -E_t/E_x but image noisy so poor method and what if E_t = 0 ? (blank area) and what if E_x = 0 ? not good either Better method: u = 1/(x_i+1 - x_i) ∫ E_i+1 dx + filtering E_t ≈ 0 u = - ∫_{x_1}^{x_2} w(x) \frac{E_x}{E_t} dx / ∫_{x_1}^{x_2} w(x) dx where W = 1/(x_2 - x_1) ∫_{x_1}^{x_2} w(x) dx Let's take w(x) = E_t u = - ∫_{x_1}^{x_2} E_t \frac{E_x}{E_t} dx / ∫_{x_1}^{x_2} E_t dx = - ∫_{x_1}^{x_2} E_x dx / ∫_{x_1}^{x_2} E_t dx not good! %? but what about w(x) = |E_t| u = - ∫_{x_1}^{x_2} |E_t| \frac{E_x}{E_t} dx / ∫_{x_1}^{x_2} |E_t| dx not optimal... discontinuities so w(x) = E_t² u = - ∫_{x_1}^{x_2} E_t² \frac{E_x}{E_t} dx / ∫_{x_1}^{x_2} E_t² dx ⊗ takes info from all the image Another way! u: E_x + E_t = 0 constraint equation ∫_{x_1}^{x_2} (uE_x + E_t)² dx <-> 0 perfect case & error real case u = min value for which ∑ d/du (∑) = 0 => ∫_{x_1}^{x_2} 2 E_x (uE_x + E_t) dx = 0 u ∫_{x_1}^{x_2} E_x² dx + ∫_{x_1}^{x_2} E_x E_t dx = 0 u = - ∫_{x_1}^{x_2} E_x E_t dx / ∫_{x_1}^{x_2} E_x² dx Least Square Solution "optical flow" Motion = constant then average on time also more accurate (2) Image projection model pinhole model f = dist. bet. hole & coo principal point 2D [Diagram: A pinhole camera model is shown with a 3D object projecting onto a 2D image plane.] x/f = X/Z y/f = Y/Z perspective projection equation Z = depth factor + scale ambiguity

Lecture 1 Notes: General Introduction, Estimating Image Motion Field, and Pinhole Camera Model

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