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

• US 10,037,592 B2
• Filed: 06/03/2016
• Issued: 07/31/2018
• Est. Priority Date: 06/05/2015
• Status: Active Grant

• Current Assignee: MindAptiv LLC
• Original Assignee: MindAptiv LLC
• Inventors: Kolb, V, John J, Granville, Kenneth
• Primary Examiner(s): Li, Ruiping
• Application Number:
  US14/999,610
• Publication Number:
  US 20160358312A1
• Time in Patent Office: 788 Days
• Field of Search: 382299
• CPC Class Codes: G06T 2207/10016 Video; Image sequence
• CPC Class Codes: G06T 2210/36 Level of detail
• CPC Class Codes: G06T 3/40 Scaling of whole images or parts thereof, e.g. expanding or contracting
• CPC Class Codes: G06T 3/4053 based on super-resolution, i.e. the output image resolution being higher than the sensor resolution
• CPC Class Codes: G06T 5/20 using local operators
• CPC Class Codes: G06T 5/73 Deblurring; Sharpening

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.

Claims

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;

2. The method of claim 1 wherein:

the digital input signal comprises a video signal comprising a plurality of two-dimensional image frames.

3. The method of claim 1 wherein:

the digital input signal comprises a two-dimensional color image signal.

4. The method of claim 1 wherein:

the digital input signal comprises an audio signal.

5. A system for improving the detail of a digital input image signal comprising:

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;

6. The system of claim 5 wherein:

the digital input signal comprises a video signal comprising a plurality of two-dimensional image frames.

7. The system of claim 5 wherein:

the digital input signal comprises a two-dimensional color image signal.

8. The system of claim 5 wherein:

the digital input signal comprises an audio signal.

9. The system of claim 5 wherein:

the system further comprises a display;

the output unit transmits the digital output image signal to the display; and

the digital output image signal is presented as an image on the display.

10. The system of claim 5 wherein:

the polynomial equation comprises a quadratic term.

11. The system of claim 5 wherein:

the polynomial equation comprises a piecewise quadratic equation.

12. The system of claim 5 wherein:

the digital output signal comprises a digital image signal having detail of at least a 4K video signal in at least one portion.

13. The system of claim 5 wherein:

the system is implemented as part of a computer web browser.

14. The system of claim 5 wherein:

the system is configured for operating on a multi-processor computer; and

the computation unit is configured for parallel processing of quaternion logarithm calculations on the multi-processor computer.

15. The system of claim 5 wherein:

the system further comprises a natural language dialog interface;

the digital output signal is responsive to the natural language dialog interface.

16. The system of claim 5 wherein:

the system only calculates second-order pixel gradient data at the next greater neighborhood size if the second-order pixel gradient data set is not a set of zero numbers.

17. The system of claim 5 wherein:

the digital output image signal amplitude values have a greater level of detail than the input image signal has greater detail than the digital input image signal amplitude values.

18. The system of claim 5 wherein:

the digital input image signal comprises a video signal;

the digital input image signal is processed in real time; and

the level of detail of the digital output image signal is responsive to compute resources.

19. The system of claim 5 wherein:

the system further comprises a quaternion logarithm record selection unit;

the quaternion logarithm record selection unit is configured for selecting which quaternion logarithm records to use for computation of the output digital signal; and

the quaternion logarithm selection unit is configured for selecting a quaternion logarithm record in response to the information content of the quaternion logarithm record.

20. A system for improving the detail of a digital input image signal comprising:

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;