Warped parallel nearest neighbor searches using kd-trees

Transcription

1 Warped parallel nearest neighbor searches using kd-trees Roman Sokolov, Andrei Tchouprakov D4D Technologies

2 Kd-trees Binary space partitioning tree Used for nearest-neighbor search, range search Application: surface alignment, ray-tracing

3 Building a kd-tree: median split and sliding-point rules Median split produces high aspect ratio cells more leaves to inspect

4 Building a kd-tree: median split and sliding-point rules Sliding point rule produces unbalanced trees

5 Another way to represent a kd-tree: as an hierarchy of arrays Leaves are represented as arrays of points (buckets) Nodes are represented as pointers to arrays lo hi lo lo lo hi lo hi lo hi hi lo hi hi

6 Depth first NN-search on a kd-tree 1. Starting with the root, inspect the child nodes recursively 2. Determine, on which side of the cutting plane lies the query point 3. Inspect the corresponding sub-tree, find minimal distance estimate 4. If the distance to the cutting plane is less than minimal distance, inspect the other sub-tree

7 NN-search on a kd-tree The simplest case: minimal distance found is less than the distance to all nodes

8 NN-search on a kd-tree Need to inspect the neighboring leaf

9 NN-search on a kd-tree Sometimes we have to inspect far away leaves

10 NN-search on a kd-tree using GPU Set of query points One query point per thread Problem on GPU: thread divergence 32 Threads per warp STOP GO Previous work: GPU Nearest Neighbor Searches using a Minimal kd-tree. Brown, Shoeyink GTC2010

11 Thread divergence in a warp individual threads: Path1: Path2: in a warp divergence: 2 can save a step: Path1: Path2: Path1: Path2:

12 Warped kd-tree search - To prevent divergence, all threads in a warp should perform the same operation - Use CUDA warp voting functions to decide which sub-tree to inspect first Hey, where should we go? Let s vote! We ll go left. I want to go right! OK, we ll go right later OK! I m happy now 5 6

13 Warped kd-tree search - Some threads may be inactive only active threads vote - Threads become inactive when they follow a path that does not need to be inspected Hey, where should we go? Let s vote! I ll go left (but I d hate to go right) I want to go right! (but I can go both ways) OK, we ll go right later OK! I don t care I m happy now Search is finished when all threads become inactive

14 NN-search on a kd-tree using recursion naive: inspect(node) { if (is_leaf(node)) bruteforce(node),return if (inside(node.lo)) { inspect(node.lo) if(distance_to(node.hi) < min_dist) inspect(node.hi) } else { } } warped: inspect(node, mask) { if (is_leaf(node)) bruteforce(node),return mask = mask & ballot(inside(node.lo)) if (mask) { inspect (node.lo,mask) if(any(distance_to(node.hi) < min_dist)) inspect(node.hi,mask) } else { } }

15 - Use stack to implement recursion Advantages: Warped kd-tree search - Single stack per wrap, stored in shared memory Using CUDA ballot() function: - to decide which path to follow - to create mask of active threads in a warp (requires CUDA compute capability 2.0 or greater) - A leaf on the other side of the splitting plane might have to be inspected anyway later. Might as well do it now and save time. - Single stack for all threads in a warp. Drawback: - More complex logic. Slower performance for highly divergent paths.

16 Performance evaluation 1M query and 1M search points Random points in a cube Data from 3d scans of dental models Query points: unsorted and sorted

17 Results CPU: Intel Xeon X Cores 12 Threads GPU: GK104 GeForce GTX 680 Random 3d data 3d scan data Warped Mx1M random sorted 1Mx1M random unsorted Warped Mx1M scan data sorted 1Mx1M scan data unsorted Naïve Naïve Brown Brown CPU 12 threads CPU 12 threads CPU 1 thread CPU 1 thread Time (msec) Time (msec)

18 Results CPU: Intel Xeon X Cores 12 Threads GPU: GK104 GeForce GTX 680 Random 3d data 3d scan data Warped Warped Naïve Naïve Brown Brown CPU 12 threads CPU 12 threads CPU 1 thread Mx1M random sorted 1Mx1M random unsorted CPU 1 thread Mx1M scan data sorted 1Mx1M scan data unsorted speedup over CPU 1 thread speedup over CPU 1 thread

19 time (ms) time (ms) Results Tree depth vs. bucket size: tradeoff between node traversal and brute force search CPU unsorted CPU sorted GPU unsorted bucket size bucket size

20 Future work Improve memory access to kd-tree nodes, utilize shared memory Build kd-tree on GPU Utilize inactive threads during brute-force search (reduction) Try using single stack per block