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