TELKOMNIKA ISSN: 1693-6930
Remote Sensing Image Fusion Scheme using Directional Vector in NSCT… Baohui Tian 599
capture only limited directional information, and thus cannot represent the directions of the edges accurately [6].
In recent years, Do and Vetterli developed a true two dimentsional image representation method, the Contourlet Transform CT, which is achieved by combining the Lapacian Pyramid
LP and the Directional Filter Bank DFB. Compared with the traditional DWT, CT is not only with multiscale and localization, but also with multidirection and anisotropy. As a result, CT can
represent edges and other singularities along curves much more efficiently. However, CT lacks the shift-invariance, which is desireable in many image applications such as image
enhancement, image denoising and image fusion. In 2006, Cunha et al. proposed an overcomplete transform, the NonSubsampled Contourlet Transform NSCT, which inherits the
perfect properties of CT, and possesses the shift-invariance. When the NSCT is introduced into image fusion, more information for fusion can be preserved and the impacts of mis-registration
on the fused results can also be reduced effectively. Therefore, the NSCT is more suitable for image fusion [6].
In this paper, a novel image fusion scheme using NSCT for panchromatic and multispectral images is proposed. The outline of this paper is as follows: Section 2 briefly
reviews the NSCT theory. Section 3 describes the fusion scheme in detail. Experimental results and discussion are presented in Section 4, where the proposed fusion scheme is compared with
some traditional. Lastly comes the conclusion.
2. NSCT
The NSCT is a shift-invariance version of the CT. The CT employs the LP for multiscale decomposition, and the DFB for directional decomposition. In order to get rid of the frequency
aliasing and enhance directional selectivity and shift-invariance, the NSCT eliminates the downsampling and the upsampling during the decomposition and the reconstruction of an
image; instead it is built upon coupling NonSubsampled Pyramid NSP with the NonSubsampled Directional Filter Bank NSDFB. The NSCT provides not only multiscale
analysis but also geometric and directional representation [7].
The core of the NSCT is the filter design in the nonseparable two-channel NSP and NSDFB. The goal is to design filters satisfying the Bezout identity Perfect Reconstruction, PR
and enforcing other properties such as sharp frequency response, easy implementation, regularity of the frame elements, and the tightness of the corresponding frames. Of course, if
the tightness constraint is relaxed, the FIR filters with linear phrase can also be obtained. In the NSCT, the mapping approach is adopted to design the two-channel 2-D filter banks with PR. In
addition, the filters designed with the mapping approach are factored into a ladder or lifting structure to simply computation. Therefore, the NSCT is also with a fast implementation. More
detail can be seen in [7].
The NSP, employed by the NSCT for the multiscale property, is a two-channel NSFB. The NSP is completely different from the Laplacian Pyramid LP in the CT, because it has no
downsampling or upsampling. To achieve the multiscale decomposition, the expansion is conceptually similar to the 1-D à trous and has
1 J
redundancy, where J denotes the number of decomposition levels. The ideal frequency support of the lowpass filter at j -th stage is the
region
2
[ 2 , 2 ]
j j
. Accordingly, the ideal support of the equivalent highpass filter is the complement of the lowpass on the
1 1
2 2
[ 2
, 2 ] \ [
2 , 2 ]
j j
j j
region. The filters for subsequent stages are obtained by upsampling the filters of the first stage with the sampling
matrix. The structure is thus different from the tensor product à trous. In particular, one bandpass image is produced at each stage resulting in
1 J
redundancy. The NSDFB is a shift-invariance version of the critically sampled DFB in the CT. It is
constructed by eliminating the downsampling and the upsampling in the DFB. The building block of the NSDFB is also a two-channel NSFB. However, the ideal frequency response for the
NSDFB is different. The upsampling of all filters is based on quincunx matrix. The higher level decompositions follow the similar strategy.
The NSCT is flexible in that it allows any number of
2
l
directions in each scale, where
l
denotes a positive integer. In particular, it can satisfy the anisotropic scaling law and has
ISSN: 1693-6930
TELKOMNIKA Vol. 14, No. 2, June 2016 : 598 – 606
600 redundancy given by
1
1 2
j
J l
j
, where
j
l
denotes the number of direction decomposition levels in NSDFB at the j -th scale.
a Panchromatic image b Multispectral image
c Fused image using DWT-based method d Fused image using SWT-based method
e Fused image using DTCWT-based method
f Fused image using CT-based method
g Fused image using NSCT-based method h Fused image using the proposed scheme
Figure 1. Source images and the fused images 256256 pixels
TELKOMNIKA ISSN: 1693-6930
Remote Sensing Image Fusion Scheme using Directional Vector in NSCT… Baohui Tian 601
3. Proposed Fusion Scheme
