Vectoral Representations of the Multi-Spectral Images and Its Arithmetic Processing

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  • 多重分光画像のベクトル表現とその演算処理
  • タジュウ ブンコウ ガゾウ ノ ベクトル ヒョウゲン ト ソノ エンザン ショ

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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.<br>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.<br>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.<br>1) Let U and V be normalized multispectral images in the same area at different times.<br>Then, W becomes a monochrome image enhancing most the time invariant region of the spectral characteristics in the area.<br>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.<br>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.<br>1) Let P1, …, Pr be normalized multispectral images in the same area at different times.<br>Then, K becomes a tensoral image eliminating the time invariant region of the spectral characteristics in the area.<br>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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