1147 
A SPATIAL DOMAIN AND FREQUENCY DOMAIN INTEGRATED APPROACH TO 
FUSION MULTIFOCUS IMAGES 
J. Yang, Y. Ma, W. Yao, W. T. Lu 
Institute of atmospheric sounding, Chinese Academy of Meteorological Sciences, Beijing, P. R. China 
- yangjunlOO@gmail.com, maying@cams.cma.gov.cn, yaowen@cams.cma.gov.cn, wtlu@ustc.edu 
KEY WORDS: multifocus, image fusion, Sum-modified-Laplacian, stationary wavelet transform 
ABSTRACT: 
A spatial domain and frequency domain integrated approach was proposed to fusion multifocus images. The proposed multifocus 
image fusion algorithm was composed of computing Sum-modified-Laplacian(SML) for each focus image, stationary wavelet 
transform(SWT) decomposition, image fusion and inverse SWT. Firstly, two initial binary decision maps were created by setting two 
thresholds to the SML difference between two focus images. Secondly, two different focus images were decomposed using SWT 
transform separately, then in the SWT domain of the two transformed images, the new SWT coefficients were acquired by adopting a 
simple fusion rule. Low-bands coefficients were integrated using the weighted average, and high-bands coefficients were integrated 
using choose max and the two SML maps. Finally the fused image was obtained by performing an inverse SWT transform. Two 
groups of different focus images were performed to evaluate the performance of our method. Experimental results showed that our 
algorithm can provide better performance than the wavelet method from both visual perception and quantitative analysis. 
1. INTRODUCTION 
Due to the limited depth-of-focus of optical lenses, it is often 
difficult to get an image that contains all relevant objects in 
focus. Multifocus image fusion methods are developed to solve 
this question. There are various approaches have been 
performed in the literatures. These approaches can be divided 
into two types, spatial domain method and frequency domain 
method. 
Spatial domain fusion method is performed directly on the 
source images. Weighted average is the simplest spatial domain 
method, which needn’t any transformation or decomposition on 
the original images. The merit of this method is simple and fit 
for real-time processing, but simple addition will reduce the 
signal-to-noise of the result image. Improved method is to 
compute the degree of focus for each pixel use various focus 
measures in multifocus images. A focus measure is defined 
which is a maximum for the best focused image and it 
generally decreases as the defocus increases (Krotkov,1987). 
Many focus measures techniques have been implemented in 
literatures, such as gray level variance(GLV) (Tyan,1997), 
Energy of image gradient(EOG), Energy of Laplacian of the 
image(EOL) (Huang and Jing, 2007), 
Sum-modified-Laplacian(SML) (Nayar and Nakagawa, 1994), 
Tenenbaum’s algorithm(Tenengrad) and so on. Pixels with 
maximum focus measures are selected to construct and form 
ultimate all-in-focus image. The most commonly reported 
problem in this technique is from blocking effects. 
In frequency domain methods, the input images are 
decomposed into multiscale coefficients initially. Various 
fusion rules are used in the selection or manipulation of these 
coefficients and synthesized via inverse transforms to form the 
fused image. Both pyramid and wavelet transforms are used as 
multiresolution filters. This type method can avoid blocking 
effects. However, many of these approaches, such as discrete 
wavelet transform(DWT) (Li et al.,1995), wavelet packet 
transform(WPT) (Yang and Zhao, 2007a) and Curvelet 
transform (Yang and Zhao,2007b), are shift-variant. So if there 
is a movement of the object in the source images or there is a 
misregistration of the source images, the performance of those 
algorithms will deteriorate. Some shift-invariant transforms are 
used to alleviate this phenomena including discrete wavelet 
frame transform(DWFT) (Li et al.,2002), dual tree complex 
wavelet transform(DT-CWT) (Ioannidou and 
Karathanassi,2007) and stationary wavelet transform(SWT) 
(Wang et al.,2003). Although these shift-invariant transforms 
are adopted, ringing effects have still been widely reported. 
In order to overcome the disadvantages of the spatial domain 
method and the frequency domain method, we proposed a 
spatial domain and frequency domain integrated approach to 
fusion multifocus images in this paper. The simulation 
experiments obtained satisfactory results. 
The next sections of this paper were organized as follows. In 
section 2 we provided a detail description of the 
Sum-modified-Laplacian and stationary wavelet transform. 
Section 3 presented our image fusion scheme. In section 4 two 
different focus images were used to evaluate our fusion 
algorithm, in the end, a conclusion was drawn in section 5. 
2. SUM-MODIFIED-LAPLACIAN AND STATIONARY 
WAVELET TRANSFORM 
LI 2.1 Sum-modified-Laplacian 
A focus measure is defined which is a maximum for the best 
focused image and it generally decreases as the defocus 
increases. Therefore, in the field of multifocus image fusion, the 
focused image areas of the source images must produce 
maximum focus measures, the defocused areas must produce 
minimum focus measures in contrast. Let f(x,y) be the gray 
level intensity of pixel {x,y). 
Nayar (1994) noted that in the case of the Laplacian the second 
derivatives in x— and y - directions can have opposite signs