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# Method for using periodicity to find consecutive scaled node positions

IP.com Disclosure Number: IPCOM000005821D
Publication Date: 2001-Nov-08
Document File: 9 page(s) / 264K

## Publishing Venue

The IP.com Prior Art Database

## Abstract

Disclosed is a method for using periodicity to find consecutive scaled node positions. Benefits include improved processing speed and accuracy of results.

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Method for using periodicity to find consecutive scaled node positions

Disclosed is a method for using periodicity to find consecutive scaled node positions. Benefits include improved processing speed and accuracy of results.

Background

The requirement for multi-dimensional scaling arises in many fields of signal and image processing where it is required to determine the value of a point in multi-dimensional space based on the known values of a set of other points, or nodes.

Interpolation is very common scheme to get the value of a scaled node set between one, two, or three pairs of its neighbor original nodes for one-, two-, or three-dimensional scaling, respectively. To find the scaled data, we must first find out scaled positions in all the dimensions in a multi-dimension system.

Because the scaling ratio could be a fractional number, the calculation of scaled positions needs many fractional numeric computations, including the time-consuming fractional multiplication.

The scaling uses the interpolation technique. It determines the value of a specified node in a space based on the known values of a set of other nodes, or points, to create a number of data based on another group of known data. Both the scaled data set and the known data set represent the same information as, for example, in an image. In other words, the information that is originally mapped to a known data set can be mapped to the scaled data set after scaling.

Each data item in these data sets can represent the value of one node, or point, in the information. The index number provides access to the data and its node position if the spaces of two consecutive nodes are known. In many applications, the space between two consecutive nodes is measured on fixed and uniformly distant grid positions. Any two consecutive items in a data set represent two consecutive nodes in that information.

In order to easily compute the scaled data, the space between any two consecutive original nodes is always assumed to be 1. Therefore, the original node position is always an integer number and its corresponding index number is always same as the node position. However, the space between any two consecutive scaled nodes and scaled node position are dependent on the scaling ratio, which may be a fraction number and is defined as the number of scaled nodes over the number of the original nodes.

For a given dimension, if the data was originally represented by

nodes and is represented by

nodes, then the scaling ratio is defined as

.

For a fixed-space node set, the more number of nodes used to represent a given information, the less the space between two consecutive nodes. If the scaling ratio equal to

, where

and

are integers, and the space between two consecutive original nodes is 1, then the space between two consecutive scaled nodes is

. The scaled positions in a given dimension, if it starts from 0, can be described by the series shown in Figure 1.

The scaled positions could be a fraction numbe...