A User-Assisted Approach to Visualizing Multidimensional Images

Abstract

Abstract-We present a new technique for fusing together an arbitrary number of aligned images into a single color or intensity image. We approach this fusion problem from the context of Multidimensional Scaling (MDS) and describe an algorithm that preserves the relative distances between pairs of pixel values in the input (vectors of measurements) as perceived differences in a color image. The two main advantages of our approach over existing techniques are that it can incorporate user constraints into the mapping process and it allows adaptively compressing or exaggerating features in the input in order to make better use of the output's limited dynamic range. We demonstrate these benefits by showing applications in various scientific domains and comparing our algorithm to previously proposed techniques.

Multidimensional Scaling

“…A single iteration of (26) consists of two steps: majorization, the construction of B s (X k ), which requires O(q 2 ) operations, and minimization, the solution of (26), which in general requires O(p 3 ) for the computation of (Φ S V s SΦ) + in the first iteration and O(p 2 ) operations in the succeeding iterations. A similar approach was carried in [26] using a subspace constructed from the data, akin to PCA, for the purpose of visualizing multidimensional images. These modifications drastically reduce the computation time of the embedding and allow the application of distance scaling to large-scale problems or within iterative procedures that require multiple applications of the SMACOF algorithm (Fig.…”

“…It is popularly used for visualization of high-dimensional signals by embedding their dissimilarities into two or threedimensional Euclidean spaces. For example, [26] uses it to visualize multidimensional images, and [36] explores multiple visualization techniques on the MNIST dataset of handwritten digits [12] (Fig. 3).…”

A Survey on Multidimensional Scaling

“…MDS can be used on multified data embedded space. MDS can be used on multified data to set number of visual channel [Hansen et al 2014;Lawrence et al 2011]…”

Three-dimensional representation of a multidimensional data set

“…In another line of research Lawrence et al describes a multi-dimensional image display method which unifies the multiple bands of a multispectral image in the visible band with a high degree of realism and maintaining the distribution characteristics of the original data values showing reduction examples from 4D, 8D and 31D spaces to the 3D space with variations in the source data that reach 1000:1 [7]. The objective is to develop a method to map an image with a large number of bands of scalar values in an image with few dimensions, or bands.…”