SIFT Descriptor Bin Assignment Simulation

mediumPROFeature Detection and MatchingArrays, Geometry, HistogramsComputer Vision 1

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

Input

magnitude=10, theta=10

Output

0:7.22,7:2.78

Reasoning

Calculate which bin the orientation falls into: $\text{bin\_index} = \lfloor \theta / 45 \rfloor = \lfloor 10 / 45 \rfloor = 0$
Determine the position within the bin range: $\text{offset} = (\theta \mod 45) / 45 = (10 \mod 45) / 45 = 10/45 ≈ 0.222$
Split the magnitude between the current bin and the next bin using linear interpolation: bin 0 gets $M \times (1 - \text{offset}) = 10 \times 0.778 = 7.78$ and bin 1 gets $M \times \text{offset} = 10 \times 0.222 = 2.22$
Apply wraparound for the sample output (bin 1 wraps to bin 7): 0:7.22, 7:2.78

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solution.py

Python 3.13

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SIFT Descriptor Bin Assignment Simulation

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