图像融合方法深度比较：GIF框架与案例研究

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本文《2005年图像融合方法的比较分析》（A Comparative Analysis of Image Fusion Methods by Wang Zhijun）发表在IEEE Transactions on Geoscience and Remote Sensing第43卷第6期，主要探讨了如何从高分辨率的全色图像和低分辨率的多光谱图像中生成高分辨率的多光谱图像。作者通过对图像形成物理原理的深入理解，提出了一种综合框架——通用图像融合（General Image Fusion, GIF），这个框架为现有的图像融合方法分类、比较和评估提供了统一的标准。 GIF方法的核心理念是将图像融合过程与图像物理成像过程相结合，强调了高分辨率多光谱图像的像素值不仅取决于低分辨率全色图像的对应像素，而且还受到全色图像在低分辨率尺度上的近似程度的影响。这种方法将图像融合分为多个类别，其中包括但不限于： 1. **强度-色调-饱和度（Intensity-Hue-Saturation, HIS）融合**：这是一种基于色彩空间变换的方法，通过调整每个通道的权重来合并图像。 2. **Brovey变换**：利用亮度和色度的分离来增强图像细节，常用于增强多光谱图像的对比度。 3. **主成分分析（Principal Component Analysis, PCA）**：通过降低维数来提取图像的关键特征，减少冗余信息，实现数据压缩和融合。 4. **高通滤波**：利用滤波器提高图像高频信息的传递，有助于提升融合后的图像细节。 5. **高通调制和à trous算法**：这些方法涉及信号处理技术，如滤波后进行信号增强或频域操作，以增强图像的特定特征。文章通过GIF框架对这些方法进行了深入分析，指出它们各自的优点和局限性，这对于图像处理领域的研究人员来说，提供了一个全面而实用的学习和研究工具，帮助他们更好地理解和选择合适的图像融合策略。此外，该研究也为图像处理技术的发展和改进奠定了理论基础，特别是在遥感和地理信息系统（GIS）应用中的多源数据融合场景。

WANG et al.: A COMPARATIVE ANALYSIS OF IMAGE FUSION METHODS 1393

a high-resolution pixel as a pure unit surface on which the re-

ﬂectance

and the solar incidence angle are uniform. From

(1), we have

(2)

Since each low-resolution pixel value (or radiance) can be

treated as a weighted average of high-resolution pixel values (or

radiances) over the corresponding space, provided that only the

uniformly weighted case is considered for the sake of simplicity,

we have

(3)

However, for pixel-level image fusion, it is necessary to

sample the low-resolution image and the high-resolution

image at the same pixel size. The low-resolution mother pixel

is thus replaced with 16 child pixels at 1-m pixel

size, whose pixel values may be considered to be the same

as the DN

, for the sake of simpliﬁcation, and denoted as

DN . Then the one-to-one relationship

between the pixels of the high-resolution image and the pixels

of the low-resolution image is established at 1-m pixel size

(see Fig. 1). If we divide the corresponding pixel values of the

same band high-resolution and low-resolution images, then

is cancelled. We obtain

(4)

Within a low-resolution image, pixels can be classiﬁed as

pure pixels and mixed pixels. Pure pixels correspond to the

interior pixels (homogeneous regions), which originate from

the same type of high-resolution pixels. The spatial difference

between the high-resolution pixels and the corresponding pure

low-resolution pixels is caused by the cosine factor. Mixed

pixels correspond to the boundary pixels (heterogeneous re-

gions), which originate from different types of high-resolution

pixels. The spatial difference between the high-resolution

pixels and the corresponding mixed low-resolution pixels is

caused by both reﬂectance and cosine variations.

For pure low-resolution pixels, we have

(5)

Equation (4) thus becomes

(6)

Equation (6) shows that the ratio between DN

and

is controlled by the cosine factor and is independent

of the sensor band. It is worth mentioning that independence

of the sensor band is only approximately true. Perfect inde-

pendence of the sensor band is never achieved because image

formation in reality is far more complex than the simpliﬁed

image formation model.

If PAN represents a panchromatic band and MS a multispec-

tral band, then from (6), for

PAN and MS, we have

(7)

Manipulating (7) yields the equivalent expression

DN (8)

In practice, DN

, the pixel values of the HRPI, and

, the corresponding pixel values of the upsam-

pled LRMI, are known. DN

, the pixel values of the

low-resolution panchromatic image (LRPI), and DN

the pixel values of the HRMI, are unknown. However, as long

as DN

is approximated, DN can be solved for.

The mathematical model itself is the same as the HPM method

and has also appeared in many other papers, such as those of

[19], [20], andd [33]. However, different methods are used to

compute DN

in those papers.

Since (8) can lead to an ill-posed situation if DN

, introducing two intermediate parameters and in (8) gives

DN (9)

where

DN DN DN

DN when DN and is set to 1 when

. Parameter is the signal difference be-

tween the HRPI and the LRPI. It represents the detail informa-

tion between the high- and low-resolution levels. Parameter

is the modulation coefﬁcient for the detail information. It deter-

mines how the detail information of the HRPI is injected into

the LRMIs.

For mixed low-resolution pixels, (7) does not always hold.

One solution in this case is to subdivide these pixels into sev-

eral homogeneous sections according to the information from

high-resolution pixels; (7) will then hold true within each ho-

mogeneous section. However, it is hard to un-mix the spectral

properties

of these pixels when the HRPI has only one spec-

tral band. For the sake of simplicity, we assume that (7) holds

true for these pixels as well, so that spatial information caused

by variations in reﬂectance is restored in the same way as that

resulting from cosine variation.

Equation (9) is considered as the mathematical model of the

GIF method. It shows that the pixel values of the HRMIs are

determined by the corresponding pixel values of the LRPI, or,

say, by the corresponding detail information of the panchro-

matic band and the modulation coefﬁcients. The performance

of the fusion process is therefore determined by how the LRPI

is computed and how the modulation coefﬁcients are set.

It is also worth mentioning that, while the GIF method is de-

rived based on the IKONOS sensor, it is also applicable to other

sensors where the calibration coefﬁcient offset in (1) is zero. For

those sensors whose offset is not equal to zero, the DN must be

calibrated to the radiance or, at least, the offset must be cali-

brated from the DN in order to make the GIF method hold true.

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