Digital quaternion logarithm signal processing system and method for images and other data types

摘要

A system and method for improving the detail of an input digital signal, such as a signal comprising a two dimensional image, can be implemented by computing first and second order gradients of the input signal. These gradients can be represented as quaternions. The logarithm of the quaternions can be used to determine the magnitude and orientation of gradient vectors in the input signal. This gradient magnitude and gradient orientation information can be used to construct an output digital signal that has greater detail than the input digital signal.

主权项

1. A method for improving the detail of a digital input signal comprising the steps of:
receiving a digital two-dimensional image input signal that comprises pixel information records wherein:
a pixel information record comprises a pixel x-location field, a pixel y-location field, and a pixel value field;the pixel x-location field specifies an x-location in a Cartesian coordinate space for a pixel;the pixel y-location field specifies a y-location in the Cartesian coordinate space for the pixel; andthe pixel values field comprises an amplitude value that is responsive to a brightness of the pixel; computing second-order gradient data sets for at least a portion of the pixel records by:
selecting a center pixel from the pixel information records;selecting a neighborhood size from the group comprising 1, 2, 4, 8, and 16 increments;computing a first-order-pixel gradient data set before computing a second-order pixel gradient data set; andcomputing the second-order gradient data sets for smaller neighborhood sizes before computing the second-order gradient data sets for larger neighborhood sizes; wherein:
a first-order gradient data set comprises computed first-order gradient values for neighboring pixels around the center pixel;a neighboring pixel is a pixel in the pixel information records that is no further from the center pixel than the neighborhood size;the distance from the center pixel to the neighboring pixel is measured in increments;an increment comprises a movement selected from the group of:
movement to an adjacent vertical y-direction pixel;movement to an adjacent horizontal x-direction pixel; andmovement to pixel that is horizontally adjacent to an adjacent vertical pixel; anda first-order gradient value is calculated using the equation:FOG=ΔI(ΔXP)2+(ΔYP)2 where:
FOG=the first order gradient value;ΔI=the neighboring pixel value minus the center pixel value;ΔXP=the neighboring pixel x-location minus the center pixel x-location; andΔYP=a neighboring pixel y-location minus the center pixel y-location;a second-order gradient data set comprises computed second-order gradient values;the second-order gradient values are calculated for pixel pairs;pixel pairs are comprised of two neighboring pixels that are adjacent to each other whose first-order gradient values have been calculated;a second-order gradient value for a pixel pair is computed using the equation:SOG=ΔFOG(ΔXPP)2+(ΔYPP)2 where:
SOG=a second-order gradient value;ΔFOG=a difference in first order gradient values between a neighboring pixel and an adjacent neighboring pixel;ΔXPP=a difference in x-locations between the neighboring pixel and the adjacent neighboring pixel; andΔYPP=a difference in y-locations between the neighboring pixel and the adjacent neighboring pixel; converting a plurality of second-order gradient data sets to quaternions wherein the quaternions comprise imaginary quaternion portions and real quaternion portions; calculating quaternion logarithms from the quaternions; determining first quaternion logarithm values from the quaternion logarithms wherein the first quaternion logarithm values are responsive to the magnitude of the quaternion logarithms; determining second quaternion logarithm values from the quaternion logarithms wherein the second quaternion logarithm values are responsive to the orientation of the quaternion logarithms; creating a plurality of pixel quaternion logarithm records that each comprise:
a pixel x-location field for storing the x-location value for the center pixel of the second-order gradient data set from which the first quaternion logarithm value and the second quaternion logarithm value were computed;a pixel y-location field for storing a y-location value for the center pixel of the second-order gradient data set from which the first quaternion logarithm value and the second quaternion logarithm value were computed;a neighborhood size field for storing the neighborhood size of the second-order gradient data set from which the first quaternion logarithm value and the second quaternion logarithm value were computed;a first quaternion logarithm field for storing the first logarithm quaternion logarithm value; anda second quaternion logarithm field for storing the second quaternion logarithm value; and selecting which quaternion logarithm records to use for further computation in response to the information content of a quaternion logarithm record; and generating an output digital signal in response to the quaternion logarithm records, wherein;
the output digital signal has greater detail than the digital two-dimensional input signal, andgenerating further comprises using a polynomial equation.