Digital quaternion logarithm signal processing system and method for images and other data types
First Claim
Patent Images
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; and
the 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; and
computing 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; and
movement to pixel that is horizontally adjacent to an adjacent vertical pixel; and
a first-order gradient value is calculated using the equation;
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Abstract
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.
72 Citations
20 Claims
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1. A method for improving the detail of a digital input signal comprising the steps of:
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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; and the 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; and computing 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; and movement to pixel that is horizontally adjacent to an adjacent vertical pixel; and a first-order gradient value is calculated using the equation; - View Dependent Claims (2, 3, 4)
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5. A system for improving the detail of a digital input image signal comprising:
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a computer memory unit for storing the digital input image signal wherein; the memory unit is configured for storing the digital input image signal as pixel information records; 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; and the pixel values field comprises a value that is responsive to a brightness of the pixel; a computation unit that; selects a center pixel from the pixel information records; selects a neighborhood size from the group comprising 1, 2, 4, 8, and 16 increments; computes a first-order-pixel gradient data set corresponding to a center pixel and a neighborhood size wherein; the computation unit computes a first-order pixel data set for a center pixel at a smaller neighborhood size before computing a first-order pixel data set at a larger neighborhood size; the 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; and movement to pixel that is horizontally adjacent to an adjacent vertical pixel; and a first-order gradient value is calculated using the equation; - View Dependent Claims (6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19)
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20. A system for improving the detail of a digital input image signal comprising:
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a computer-readable memory; a program stored on the computer-readable memory and adapted to be executed on a processor wherein the computer program is configured for performing the following operations; storing the digital input image signal as 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; and the pixel values field comprises a value that is responsive to a brightness of the pixel; 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 corresponding to a center pixel and a neighborhood size wherein; the program computes a first-order pixel data set for a center pixel at a smaller neighborhood size before computing a first-order pixel data set at a larger neighborhood size; the 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; and movement to pixel that is horizontally adjacent to an adjacent vertical pixel; and a first-order gradient value is calculated using the equation;
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Specification