Update:
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2021-07-14: Optimize memory usage. Now a 2000x2000 image with 64 control points spend about 4.2GB memory. (20GB in the previous version)
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2020-09-25: No need for so-called inverse transformation. Just transform target pixels to the corresponding source pixels.
Moving least squares is a method of reconstructing continuous functions from a set of unorganized point samples via the calculation of a weighted least squares measure biased towards the region around the point at which the reconstructed value is requested.
In computer graphics, the moving least squares method is useful for reconstructing a surface from a set of points. Often it is used to create a 3D surface from a point cloud through either downsampling or upsampling.
- Affine deformation
- Similarity deformation
- Rigid deformation
- Toy
- Monalisa
- Cells (Download data)
The original label is overlapped on the deformed labels for better comparison.
img_utils.py: Implementation of the algorithmsimg_utils_demo.py: Demo program
- Here lists some examples of memory usage and running time
| Image Size | Control Points | Affine | Similarity | Rigid |
|---|---|---|---|---|
| 500 x 500 | 16 | 0.57s / 0.15GB | 0.99s / 0.16GB | 0.89s / 0.13GB |
| 500 x 500 | 64 | 1.6s / 0.34GB | 3.7s / 0.3GB | 3.6s / 0.2GB |
| 1000 x 1000 | 64 | 7.7s / 1.1GB | 17s / 0.98GB | 15s / 0.82GB |
| 2000 x 2000 | 64 | 30s / 4.2GB | 65s / 3.6GB | 69s / 3.1GB |
- Estimate memory usage for large image: (h x w x N x 4 x 2) x 2~2.5
- h, w: image size
- N: number of control points
- 4: float32
- 2: coordinates (x, y)
- 2~2.5: intermediate results
[1] Schaefer S, Mcphail T, Warren J. Image deformation using moving least squares[C]// ACM SIGGRAPH. ACM, 2006:533-540.