ROTHSTEIN CODE TRANSFORMATIONS AS A DIGITAL OPTICAL SCALING METHOD

Azar Peter Dagher

doi:10.15282/ijsecs.6.2.2020.2.0070

Abstract

The Rothstein code data transformation method is a largely forgotten and underutilized method originally theorized from optics and retinal recruitment. The code is a binary representation of the slope of a line or scaling factor and can transform data and images similar to matrix multiplications except with built-in interpolations. The theoretical validation of the method presented in the original publications is complex. The purpose of this paper is to borrow from quantum theory and dual nature of light, particle and wave, to simplify the theoretical understanding. With this understanding, the method becomes more intuitive in the example applications that follow. These application examples include digital resampling of data for signal processing applications, examples for matrix scaling such as for the management of discordant data sets, and for image processing.

Highlights

ROTHSTEIN CODE TRANSFORMATIONS AS A DIGITAL OPTICAL SCALING METHODABSTRACT – The Rothstein code data transformation method is a largely forgotten and underutilized method originally theorized from optics and retinal recruitment
Affine transformations of data (Schneider, and Eberly, 2003), such as images, have been the mainstay of data scaling, an operation that requires the two steps of matrix multiplication followed by the interpolation of data, to smooth out distortions or fill in the gaps from the matrix operation
We present the theoretical validation of the method using the particle theory of light passing through a lens

Summary

ROTHSTEIN CODE TRANSFORMATIONS AS A DIGITAL OPTICAL SCALING METHOD

ABSTRACT – The Rothstein code data transformation method is a largely forgotten and underutilized method originally theorized from optics and retinal recruitment. The code is a binary representation of the slope of a line or scaling factor and can transform data and images similar to matrix multiplications except with built-in interpolations. The purpose of this paper is to borrow from quantum theory and dual nature of light, particle and wave, to simplify the theoretical understanding. With this understanding, the method becomes more intuitive in the example applications that follow. KEYWORDS Rothstein code, interpolation, data transformations, optics, photons

INTRODUCTION

OPTICAL THEORETICAL BASIS

EXAMPLE APPLICATIONS

Resizing Discordant Data for Matrix Operations

The sum of these matrices

CONCLUSION