doi:10.1016/S0167-8655(02)00152-6
Copyright © 2002 Elsevier Science B.V. All rights reserved.
A new wavelet-based measure of image focus
a Department of Mathematics and Statistics, Flinders University of South Australia, GPO Box 2100, Adelaide, SA 5001, Australia
b Institute of Information Theory and Automation, Academy of Sciences of the Czech Republic, Pod vodárenskou v

í 4, 18208, Prague 8, Czech Republic
c Astronomical Institute, Academy of Sciences of the Czech Republic, 25165, Ond

ejov, Czech Republic
Received 6 November 2001;
revised 28 January 2002.
Available online 24 May 2002.
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Abstract
We present a new measure of image focus. It is based on wavelet transform of the image and is defined as a ratio of high-pass band and low-pass band norms. We show this measure is monotonic with respect to the degree of defocusation and sufficiently robust. We experimentally illustrate its performance on simulated as well as real data and compare it with existing focus measures (gray-level variance and energy of Laplacian). Finally, an application of the new measure in astronomical imaging is shown.
Author Keywords: Image blurring; Focus measure; Wavelet transform; Astronomical imaging
Fig. 1. Four examples of our test images: Lena blurred by 3×3 averaging mask with slight additive noise of STD=5 (top left), the same with heavy noise (STD=30) (top right), blurring by 9×9 mask with slight noise (bottom left), both heavy blurring and noise (bottom right).
Fig. 2. Energy of Laplacian M5 calculated on Lena image for various amount of blurring and noise.
Fig. 3. Focus measure W calculated on Lena image for various amount of blurring and noise. Daubechies wavelet of 10 taps and the decomposition depth 1 was used.
Fig. 4. Focus measure W calculated on Lena image for various amount of blurring and noise. Daubechies wavelet of 10 taps and the decomposition depth 2 was used.
Fig. 5. Indoor scene: Focused image (top left), slight out-of-focus (top right), medium out-of-focus (bottom left), heavy out-of-focus (bottom right).
Fig. 6. Six consecutive sunspot images corrupted by variable blurring caused by atmospheric turbulence.
Table 1. Various focus measures calculated for the indoor images depicted in Fig. 5. Proportional values are used, 1 stands for the best focused image in the sequence

Table 2. Various focus measures calculated for the sunspot images in Fig. 6. Proportional values are used, 1 stands for the best image in the sequence
