Integral Image-Based Differential Filters

We describe a relationship between integral images and
differential images. First, we derive a simple difference filter from
conventional integral image. In the derivation, we show that an
integral image and the corresponding differential image are related
to each other by simultaneous linear equations, where the numbers
of unknowns and equations are the same, and therefore, we can
execute the integration and differentiation by solving the simultaneous
equations. We applied the relationship to an image fusion problem,
and experimentally verified the effectiveness of the proposed method.

• Kohei Inoue
• Kenji Hara
• Kiichi Urahama

• Integral images
• differential images
• differential filters
• image fusion.

[1] R. C. Gonzalez and R. E. Woods, Digital Image Processing,
Addison-Wesley Publishing Company, Inc., 1992.
[2] W. K. Pratt, Digital Image Processing, 3rd ed., John Wiley & Sons, Inc.,
2001.
[3] P. Viola and M. J. Jones, "Robust Real-Time Face Detection,” Int. J.
Comput. Vision, vol. 57, no. 2, pp. 137–154, May 2004.
[4] F. Porikli, "Integral histogram: a fast way to extract histograms in
Cartesian spaces,” Proc. CVPR, vol. 1, pp. 829–836, 2005.
[5] A. Alonso-Gonz´alez, C. L´opez-Mart´ınez, P. Salembier, and X. Deng,
"Bilateral Distance Based Filtering for Polarimetric SAR Data,” Remote
Sens., vol. 5, no. 11, pp. 5620–5641, 2013.
[6] S. Savic, "Multifocus Image Fusion Based on Empirical Mode
Decomposition,” Twentieth International Electrotechnical and Computer
Science Conference, ERK 2011.