imgproc: optimize EMD (Earth Mover's Distance) solver performance #29194
### imgproc: optimize EMD solver performance using O(V) spanning tree traversal
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This PR significantly optimizes the performance of the Earth Mover's Distance (`cv::EMD`) solver in `modules/imgproc/src/emd_new.cpp`.
Specifically, it refactors the dual-variable calculation in `EMDSolver::findBasicVars()` from a naive $O((N+M)^2)$ linked-list scanning approach to an optimized $O(N+M)$ BFS tree traversal utilizing existing adjacency lists, leading to a massive speedup.
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#### Technical Details & Core Bottleneck Fixed
1. **Algorithmic Complexity Reduction in `findBasicVars()`:**
- **Before**: The original implementation solved the dual variables $u_i$ and $v_j$ by traversing the entire unmarked rows (`u0_head`) or columns (`v0_head`) linked-lists and invoking `getIsX(i, j)` inside nested loops to find connected basic variables. This resulted in an $O((N+M)^2)$ complexity per simplex iteration. For a scale of $2000 \times 2000$, this performed up to $16,000,000$ operations per iteration.
- **After**: Since `EMDSolver` already maintains the adjacency lists of the basic variables tree (`rows_x` and `cols_x`), we can traverse the spanning tree in linear time. This PR implements a dual-queue BFS tree traversal. The complexity per iteration is drastically reduced to $O(N+M)$, performing at most $4000$ operations per iteration.
2. **Cache Locality & Pointer-Chasing Elimination:**
- Replaced pointer-chasing on dynamically-allocated linked lists with contiguous, stack-allocated array queues (`cv::AutoBuffer`), significantly improving CPU L1/L2 cache hit rates and enabling hardware prefetching.
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#### Performance Benchmarks
Below is the benchmark comparison evaluated on a standard CPU.
#### Test 1: dims = 64
| Scale ($N, M$) | Original EMD (ms) | Optimized EMD (This PR) | Speedup |
| :--- | :--- | :--- | :--- |
| **100** | 5.473 | 3.419 | **1.60x** |
| **500** | 381.871 | 244.355 | **1.56x** |
| **1000** | 1893.053 | 1369.016 | **1.38x** |
| **2000** | 11387.792 | 8331.221 | **1.37x** |
#### Test 2: dims = 3
| Scale ($N, M$) | Original EMD (ms) | Optimized EMD (This PR) | Speedup |
| :--- | :--- | :--- | :--- |
| **100** | 4.433 | 3.042 | **1.46x** |
| **500** | 365.762 | 259.735 | **1.41x** |
| **1000** | 1989.400 | 1421.952 | **1.40x** |
| **2000** | 12731.836 | 7952.210 | **1.60x** |
*(Note: The exact performance figures may vary slightly depending on the compiler and test machine.)*
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#### Verification
- All existing tests in `opencv_test_imgproc` (including EMD tests) pass successfully. No regressions were introduced.
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### Pull Request Readiness Checklist
See details at https://github.com/opencv/opencv/wiki/How_to_contribute#making-a-good-pull-request
- [x] I agree to contribute to the project under Apache 2 License.
- [x] To the best of my knowledge, the proposed patch is not based on a code under GPL or another license that is incompatible with OpenCV
- [x] The PR is proposed to the proper branch
- [ ] There is a reference to the original bug report and related work
- [ ] There is accuracy test, performance test and test data in opencv_extra repository, if applicable
Patch to opencv_extra has the same branch name.
- [ ] The feature is well documented and sample code can be built with the project CMake
Ding zhehao