diff --git a/docs/notes/iou3d.md b/docs/notes/iou3d.md index 8cc176de..cc9f6c19 100644 --- a/docs/notes/iou3d.md +++ b/docs/notes/iou3d.md @@ -16,7 +16,7 @@ In 2D, IoU is commonly applied to axis-aligned boxes, namely boxes with edges pa In 3D, boxes are usually not axis aligned and can be oriented in any way in the world. We introduce a new algorithm which computes the *exact* IoU of two *oriented 3D boxes*. -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*. +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*. In 3D, these planar units are 3D triangular faces. In 2D, they are 2D edges. Each planar unit belongs strictly to either `box1` or `box2`. @@ -46,12 +46,12 @@ The intersection shape is formed by the convex hull from the intersection points Our algorithm has several advantages over Objectron's: -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. -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. -3. Our implementation supports batching, unlike Objectron which assumes single element inputs for `box1` and `box2`. -4. Our implementation is easily parallelizable and in fact we provide a custom C++/CUDA implementation which is **450 times faster than Objectron**. +* 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. +* 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. +* Our implementation supports batching, unlike Objectron which assumes single element inputs for `box1` and `box2`. +* Our implementation is easily parallelizable and in fact we provide a custom C++/CUDA implementation which is **450 times faster than Objectron**. -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`. +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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