Efficient keypoint detection and description via polynomial regression of scale space

Keypoint detection and description using approximate continuous scale space are more efficient techniques than typical discretized scale space for achieving more robust feature matching. However, this state-of-the-art method requires high computational complexity to approximately reconstruct, or decompress, the value at an arbitrary point in scale space. Specifically, it has O(M2) computational complexity where M is an approximation order. This paper presents an efficient scale space approach that provides decompression operation with O(M) complexity without a loss of accuracy. As a result of the fact that the proposed method has much fewer variables to be solved, the least-square solution can be obtained through normal equation. This is easier to solve than the existing method which employs Karhunen-Loeve expansion and generalized eigenvalue problem. Experiments revealed that the proposed method performs as expected from the theoretical analysis.