TY - GEN
T1 - Universal Approach for DCT-Based Constant-Time Gaussian Filter with Moment Preservation
AU - Sugimoto, Kenjiro
AU - Kyochi, Seisuke
AU - Kamata, Sei Ichiro
N1 - Funding Information:
This work was supported by JSPS KAKENHI (Grant Number: JP16K16092, JP17H01764).
PY - 2018/9/10
Y1 - 2018/9/10
N2 - This paper presents a universal approach for constant-time Gaussian filters (O(1) GF) based on the Discrete Cosine Transform (DCT). It is well known that DCT has the eight types of definitions. Existing methods of O(1) GF use difference DCT type according to their original concepts. However, all types of DCT have not been studied comprehensively and quantitatively. Unlike existing methods, the proposed approach covers all types of DCT and moment preservation for arbitrary orders, which enables us to clarify differences of O(1) GF derived from each DCT through a comprehensive analysis. Based on the universal approach, a closed-form solution to optimize weight coefficients is also proposed based on a simple convex analysis. Experiments found that DCT-7 shows the highest approximate accuracy, which is a new conclusion different from existing methods.
AB - This paper presents a universal approach for constant-time Gaussian filters (O(1) GF) based on the Discrete Cosine Transform (DCT). It is well known that DCT has the eight types of definitions. Existing methods of O(1) GF use difference DCT type according to their original concepts. However, all types of DCT have not been studied comprehensively and quantitatively. Unlike existing methods, the proposed approach covers all types of DCT and moment preservation for arbitrary orders, which enables us to clarify differences of O(1) GF derived from each DCT through a comprehensive analysis. Based on the universal approach, a closed-form solution to optimize weight coefficients is also proposed based on a simple convex analysis. Experiments found that DCT-7 shows the highest approximate accuracy, which is a new conclusion different from existing methods.
KW - Constant-time Gaussian filter
KW - Discrete cosine transform
KW - Moments
KW - Sliding transform
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U2 - 10.1109/ICASSP.2018.8461679
DO - 10.1109/ICASSP.2018.8461679
M3 - Conference contribution
AN - SCOPUS:85054278240
SN - 9781538646588
T3 - ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
SP - 1498
EP - 1502
BT - 2018 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2018 - Proceedings
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 2018 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2018
Y2 - 15 April 2018 through 20 April 2018
ER -