Abstract
This paper address the problem of rotation matrix sampling used for multidimensional probability distribution transfer. The distribution transfer has many applications in remote sensing and image processing such as color adjustment for image mosaicing, image classification, and change detection. The sampling begins with generating a set of random orthogonal matrix samples by Householder transformation technique. The advantage of using the Householder transformation for generating the set of orthogonal matrices is the uniform distribution of the orthogonal matrix samples. The obtained orthogonal matrices are then converted to proper rotation matrices. The performance of using the proposed rotation matrix sampling scheme was tested against the uniform rotation angle sampling. The applications of the proposed method were also demonstrated using two applications i.e., image to image probability distribution transfer and data Gaussianization.
Highlights
In remote sensing, the analysis of multi-temporal data is widely used in many applications such as urban expansion monitoring, deforestation, change detection, and agriculture monitoring
We demonstrate the effectiveness of the mul(10) tidimensional probability distribution transfer
We proposed to use the Householder transformation to uniformly sampling the orthogonal matrices first and transform the orthogonal matrices to rotation matrices
Summary
The analysis of multi-temporal data is widely used in many applications such as urban expansion monitoring, deforestation, change detection, and agriculture monitoring. Its goal is to transfer statistical properties by reshaping the probability distribution of the source image such that its shape is matched with that of a reference one. Is based on the Monge’s transport problem which is to find minimal displacement for mass transportation The solution from this linear approach can be used as initial solution for non-linear probability distribution transfer methods. In (Pitieet al., 2007), an iterative method for transforming the probability distribution of an RGB image was proposed. The concept of this approach is to rotate data space using a random rotation matrix and perform 1D distribution transfer on each axe of the new coordinate system. R i.e., Xrs(k) ← RXs(k − 1) and Xrt ← RXt; 4 Perform 1-D histogram matching on each of the axis in the rotated space;
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