Arithmetic processing of remotely sensed multispectral images has been based on statistical methods so far. In the present paper, a method of the image processing is discussed from algebraic point of view.
First, spectral characteristics of energy intensity and reflectance are considered to be expressible by a vector which is called the spectral vector. Next, if (
l, m) pixels of the image
P are scalar, vector or tensor quantities, then
P is called a scalar, vectoral or tensoral image respectively. For example, a monochrome image, a multispectral image and an exterior product image are scalar, vectoral and tensoral images respectively.
Let
U and
V be vectoral images. The inner product between
U and
V gives a scalar image
W. If
U and
V are multispectral images, the inner product image
W and the inner product operation have the following peculiarities.
1) Let
U and
V be normalized multispectral images in the same area at different times.
Then,
W becomes a monochrome image enhancing most the time invariant region of the spectral characteristics in the area.
2) Let all pixels
vlm of the
V fix the same vector. In this case, the inner product operation has a property of emphasizing filter about the spectral characteristics.
On the other hand, the exterior product of the vectoral images
P1, …,
Pr gives an image
K of which the pixels have tensor quantities of order
r. So an exterior product image
K is a tensoral image. If
P1, …,
Pr are multispectral images, the exterior product image and the exterior product operation have the following peculiarities.
1) Let
P1, …,
Pr be normalized multispectral images in the same area at different times.
Then,
K becomes a tensoral image eliminating the time invariant region of the spectral characteristics in the area.
2) Let all pixels
pjlm of the
Pj(
j=2, …,
r) fix the same vectors. In this case, the exterior product operation has a property of eliminating filter about the spectral characteristics.
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