Image Processing Reference
In-Depth Information
location equals unity. Sometimes the constant term C is included, which acts as an
offset or bias.
The most basic example of fusion is to average the input images. This leads to
select the fusion weights as w 1 (
as per Eq. ( 2.1 ).
The constant term is not used. It can be easily seen that this scheme is computa-
tionally most efficient. However, it fails to produce an output of the desired quality.
The averaging technique explicitly assumes an equal amount of information to be
present across the input images. In most examples, this is not the case. The IR image
brings out very different information from the scene that does not get captured by
a standard RGB camera. However, an average-based fusion would superimpose the
features in the IR image by the RGB image, and thus, reducing the contrast and the
information content. Therefore, an averaging-based fusion works well only when
both the inputs are similar, and, lacks contrast when the inputs are different. This
dissimilar information from multiple images causes a destructive interference which
reduces the contrast. Therefore, despite its simplicity and computational efficiency,
this method is rarely used in practice.
Fusion would be effective when the important spatial and radiometric features
from the constituent images get retained, or appropriately enhanced during the
process of fusion. Thus, one needs to extract the spatial features from images as
the first step. In order to capture the unique features in input, Toet proposed the use
of a Laplacian pyramid [172, 174]. The authors have proposed a hierarchical tech-
nique which decomposes each of the input image into a set of primitives defined by
perceptually relevant patterns. This technique generates a pyramidal decomposition
of each of the input images through filtering and subsampling the predecessor. The
successive images in the pyramid are generally the reduced versions of the input
image, and hence this representation is also referred to as the multi-resolution rep-
resentation. The successive levels of the image pyramid represent image details and
features with coarser approximations. The pyramidal representations of all the input
images are then appropriately combined at every level using a pre-defined fusion
rule. The fusion rule might be the same or different at every level, however, typically,
one comes across two sets of rules. A fusion rule defined for all but the highest level
in the pyramid is generally the same, and a different fusion rule is defined for the final
or the topmost level image in the corresponding image pyramid. However it is pos-
sible to have a combination of more fusion rules. The combining process generates
an image pyramid where each level represents the fusion of images at that particular
level. The final resultant image can then be reconstructed by applying the reverse
transformation on the fused image pyramid. Another popular pyramidal structure is
obtained by convolving the current approximation of the image with the Gaussian
filter. The pyramid so obtained is called a Gaussian pyramid. In [21], the filtering
and sampling have been combined into a single operation resulting into the Gaussian
weighted average. However, in [172], it has been argued that the linear filters alter the
intensities of the pixels near the object boundary, and therefore, their applicability
is limited when the precise measurements of the shape and size of the objects are
needed. Their scheme employs a morphological multi-resolution decomposition of
images using size-selective filters. It is claimed that morphological filters are more
) =
w 2 (
) =
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