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minor note fix
Summary: A small fix for the iou3d note Reviewed By: bottler Differential Revision: D31370686 fbshipit-source-id: 6c97302b5c78de52915f31be70f234179c4b246d
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@ -16,7 +16,7 @@ In 2D, IoU is commonly applied to axis-aligned boxes, namely boxes with edges pa
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In 3D, boxes are usually not axis aligned and can be oriented in any way in the world.
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We introduce a new algorithm which computes the *exact* IoU of two *oriented 3D boxes*.
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Our algorithm is based on the simple observation that the intersection of two oriented boxes, `box1` and `box2`, is a convex n-gon with `n > 2` comprised of connected *planar units*.
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Our algorithm is based on the simple observation that the intersection of two oriented 3D boxes, `box1` and `box2`, is a convex polyhedron (convex n-gon in 2D) with `n > 2` comprised of connected *planar units*.
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In 3D, these planar units are 3D triangular faces.
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In 2D, they are 2D edges.
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Each planar unit belongs strictly to either `box1` or `box2`.
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@ -46,12 +46,12 @@ The intersection shape is formed by the convex hull from the intersection points
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Our algorithm has several advantages over Objectron's:
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1. Our algorithm also computes the points of intersection, similar to Objectron, but in addition stores the *planar units* the points belong to. This eliminates the need for convex hull computation which is `O(nlogn)` and relies on a third party library which often crashes with nondescript error messages.
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2. Objectron's implementation assumes that boxes are a rotation away from axis aligned. Our algorithm and implementation makes no such assumption and works for any 3D boxes.
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3. Our implementation supports batching, unlike Objectron which assumes single element inputs for `box1` and `box2`.
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4. Our implementation is easily parallelizable and in fact we provide a custom C++/CUDA implementation which is **450 times faster than Objectron**.
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* Our algorithm also computes the points of intersection, similar to Objectron, but in addition stores the *planar units* the points belong to. This eliminates the need for convex hull computation which is `O(nlogn)` and relies on a third party library which often crashes with nondescript error messages.
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* Objectron's implementation assumes that boxes are a rotation away from axis aligned. Our algorithm and implementation make no such assumption and work for any 3D boxes.
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* Our implementation supports batching, unlike Objectron which assumes single element inputs for `box1` and `box2`.
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* Our implementation is easily parallelizable and in fact we provide a custom C++/CUDA implementation which is **450 times faster than Objectron**.
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Below we compare the performance for Objectron (in C++) and our algorithm, in C++ and CUDA. We benchmark for a common use case in object detection where `boxes1` hold M predictions and `boxes2` hold N ground truth 3D boxes in an image. We compute the `MxN` IoU matrix and report the time in ms for `M=N=16`.
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Below we compare the performance for Objectron (in C++) and our algorithm, in C++ and CUDA. We benchmark for a common use case in object detection where `boxes1` hold M predictions and `boxes2` hold N ground truth 3D boxes in an image and compute the `MxN` IoU matrix. We report the time in ms for `M=N=16`.
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<p align="center">
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<img src="assets/iou3d_comp.png" alt="drawing" width="400"/>
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