Geometric Computer Vision: Difference between revisions

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 ==Aperture Problem==
-When looking through a small viewport at large objects, you cannot tell which direction it is moving.
+When looking through a small viewport (locally) at large objects, you cannot tell which direction it is moving.
 See [https://www.opticalillusion.net/optical-illusions/the-barber-pole-illusion/ the barber pole illusion]
 ===Brightness Constancy Equation===
 ===Brightness Constraint Equation===
+Let <math>E(x,y,t)</math> be the irradiance and <math>u(x,y),v(x,y)</math> the components of optical flow.
+Then <math>E(x + u \delta t, y + v \delta t, t + \delta t) = E(x,y,t)</math>.
+Assume <math>E(x(y), y(t), t) = constant</math>
+==Structure from Motion Pipeline==
+===Calibration===
+# Step 1: Feature Matching
+===Fundamental Matrix and Essential Matrix===
+# Step 2: Estimate Fundamental Matrix F
+#* <math>x_i'^T F x_i = 0</math>
+#* Use SVD to solve for x from <math>Ax=0</math>: <math>A=U \Sigma V^T</math>. The solution is the last singular vector of <math>V</math>.
+#* Essential Matrix: <math>E = K^T F K</math>
+#* '''Fundamental matrix has 7 degrees of freedom, essential matrix has 5 degrees of freedom'''
+===Estimating Camera Pose===
+Estimating Camera Pose from E
+Pose P has 6 DoF. Do SVD of the essential matrix to get 4 potential solutions.
+You need to do triangulation to select from the 4 solutions.
+==Visual Filters==
+Have filters which detect humans, cars,...
+==Model-based Recognition==
+You have a model for each object to recognize.<br>
+The recognition system identifies objects from the model database.
+===Pose Clustering===
+===Indexing===
+==Texture==
+===Synthesis===
+The goal is to generate additional texture samples from an existing texture sample.
+===Filters===
+* Difference of Gradients (DoG)
+* Gabor Filters
+==Lecture Schedule==
+* 02/23/2021 - Pinhole camera model
+* 02/25/2021 - Camera calibration
+* 03/09/2021 - Optical flow, motion fields
+* 03/11/2021 - Structure from motion: epipolar constraints, essential matrix, triangulation
+* 03/25/2021 - Multiple topics (image motion)
+* 03/30/2021 - Independent object motion (flow fields)
+* 04/01/2021 - Project 3 Discussion
+* 04/15/2021 - Shape from shading, reflectance map
+* 04/20/2021 - Shape from shading, normal map
+* 04/22/2021 - Recognition, classification
+* 04/27/2021 - Visual filters, classification
+* 04/29/2021 - Midterm Exam clarifications
+* 05/04/2021 - Model-based Recognition
+* 05/06/2021 - Texture
 ==Projects==