From 544e8db71e1c32cdc20d596ba3de2d92df4b02de Mon Sep 17 00:00:00 2001 From: Trance-0 <60459821+Trance-0@users.noreply.github.com> Date: Sun, 6 Apr 2025 12:57:46 -0500 Subject: [PATCH] update --- pages/CSE559A/CSE559A_L20.md | 81 ++++++++++++++++++ .../Comparison_of_keypoint_detectors.png | Bin 0 -> 107418 bytes ...learning_for_correspondence_estimation.png | Bin 0 -> 237030 bytes 3 files changed, 81 insertions(+) create mode 100644 public/CSE559A/Comparison_of_keypoint_detectors.png create mode 100644 public/CSE559A/Deep_learning_for_correspondence_estimation.png diff --git a/pages/CSE559A/CSE559A_L20.md b/pages/CSE559A/CSE559A_L20.md index 196e089..7781656 100644 --- a/pages/CSE559A/CSE559A_L20.md +++ b/pages/CSE559A/CSE559A_L20.md @@ -62,3 +62,84 @@ For matching: ## Local feature matching ### Matching + +Simplest approach: Pick the nearest neighbor. Threshold on absolute distance + +Problem: Lots of self similarity in many photos + +Solution: Nearest neighbor with low ratio test + +![Comparison of keypoint detectors](https://notenextra.trance-0.com/CSE559A/Comparison_of_keypoint_detectors.png) + +## Deep Learning for Correspondence Estimation + +![Deep learning for correspondence estimation](https://notenextra.trance-0.com/CSE559A/Deep_learning_for_correspondence_estimation.png) + +## Optical Flow + +### Field + +Motion field: the projection of the 3D scene motion into the image +Magnitude of vectors is determined by metric motion +Only caused by motion + +Optical flow: the apparent motion of brightness patterns in the image +Magnitude of vectors is measured in pixels +Can be caused by lightning + +### Brightness constancy constraint, aperture problem + +Machine Learning Approach + +- Collect examples of inputs and outputs +- Design a prediction model suitable for the task + - Invariances, Equivariances; Complexity; Input and Output shapes and semantics +- Specify loss functions and train model +- Limitations: Requires training the model; Requires a sufficiently complete training dataset; Must re-learn known facts; Higher computational complexity + +Optimization Approach + +- Define properties we expect to hold for a correct solution +- Translate properties into a cost function +- Derive an algorithm to solve for the cost function +- Limitations: Often requires making overly simple assumptions on properties; Some tasks can’t be easily defined + +Given frames at times $t-1$ and $t$, estimate the apparent motion field $u(x,y)$ and $v(x,y)$ between them +Brightness constancy constraint: projection of the same point looks the same in every frame + +$$ +I(x,y,t-1) = I(x+u(x,y),y+v(x,y),t) +$$ + +Additional assumptions: + +- Small motion: points do not move very far +- Spatial coherence: points move like their neighbors + +Trick for solving: + +Brightness constancy constraint: + +$$ +I(x,y,t-1) = I(x+u(x,y),y+v(x,y),t) +$$ + +Linearize the right-hand side using Taylor expansion: + +$$ +I(x,y,t-1) \approx I(x,y,t) + I_x u(x,y) + I_y v(x,y) +$$ + +$$ +I_x u(x,y) + I_y v(x,y) + I(x,y,t) - I(x,y,t-1) = 0 +$$ + +Hence, + +$$ +I_x u(x,y) + I_y v(x,y) + I_t = 0 +$$ + + + + diff --git a/public/CSE559A/Comparison_of_keypoint_detectors.png b/public/CSE559A/Comparison_of_keypoint_detectors.png new file mode 100644 index 0000000000000000000000000000000000000000..cab760497de68aa69b222e920eab3fa1649f096b GIT binary patch literal 107418 zcmd43cRbhc-Ut4%$(Bgjl!nYoWsi(fq`sw+om5sRD|>~kRA`uKd>axaWPTK)jFe=L z5Fwj{-}CyO`<(ke|NkDp$M1f0&bcdn#`V6g*Xy}nSA_9FJ@!@WR#7Mvb_0DK6AFc% zg+if;U}nUh48@*X#{bZ`ndoUzo_!Sjf#1-d(LA6@q2$D}{;^`f?^#^*kGoMQ98~fj znkwgqwiL=rmVu7u5l{1<9UksS_I5G-8lQFW9xp!TJ$~vC7nku74To6Ew_#s3>ABB} zi|%DE4z<>&6>FBf&fBD)eQ(a;+JP6o9-Zo)9X>Dib8~TBR2%e62~RFk%KvzG@wV&n z5H8xtj7|UkwLJATjD>gap@08cQfd^X`QP6jqOkKA|NHL_@n&fU)Bo@9_R?(E*Z9xB 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