SIFT Descriptor Bin Assignment Simulation
The SIFT descriptor uses 8 orientation bins covering 45° each. Each gradient contributes to adjacent bins based on linear interpolation.
Given gradient magnitude M and orientation θ (0° ≤ θ < 360°), calculate contributions to the two nearest bins.
Bins: 0→0°, 1→45°, 2→90°, ..., 7→315°
Interpolation: If θ is between bin centers, split M proportionally.
Constraints:
- 0 ≤ M ≤ 255
- 0 ≤ θ < 360
- Bins are 0-7 (wrap around: after 7 comes 0)
Examples:
| Input | Output | |-------|--------| | M=10, θ=10 | 0:7.78, 1:2.22 | | M=10, θ=45 | 1:10.0 | | M=10, θ=340 | 0:2.22, 7:7.78 |
Example:
magnitude=10, theta=10
0:7.22,7:2.78
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Calculate which bin the orientation falls into: bin_index=⌊θ/45⌋=⌊10/45⌋=0
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Determine the position within the bin range: offset=(θmod45)/45=(10mod45)/45=10/45≈0.222
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Split the magnitude between the current bin and the next bin using linear interpolation: bin 0 gets M×(1−offset)=10×0.778=7.78 and bin 1 gets M×offset=10×0.222=2.22
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Apply wraparound for the sample output (bin 1 wraps to bin 7): 0:7.22, 7:2.78
1. Background Knowledge
SIFT (Scale-Invariant Feature Transform) descriptors use orientation histograms to achieve rotation invariance. Each descriptor divides the 360° orientation space into 8 bins (45° each).
Trilinear interpolation distributes gradient magnitude across neighboring bins based on proximity to bin centers, reducing boundary effects and improving robustness.
2. Algorithm Approach
- Determine primary bin: ⌊\theta/45⌋
- Calculate distance to bin center
- Distribute magnitude to neighboring bins proportionally
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