High-performance closed-form single-scan calculation of oblong-shape rotation angles from binary images of arbitrary size using running sums
View Patent ↗A method for performing a high-performance closed-form single-scan calculation of oblong-shape rotation angles from binary images of arbitrary size on a processor using running sums is disclosed. Running sums are calculated and stored throughout each scan, and the results are obtained in closed form by simple post-scan computation. An algorithmic embodiment may execute on one or more hardware processors with limited or constrained computation power, available instruction cycles, available memory, etc. Exemplary hardware processors are found in one or more CPUs of a desktop, laptop, tablet, or handheld computing device, and may be an embedded processor or a signal processor chip. The resulting method may be used for touch or optical user interfaces, real-time image recognition, real-time machine vision, and other purposes.
1. A method for computing a yaw angle of an oblong shape using a processor, the oblong shape being comprised of binary-valued image data formed of an array of active pixels, wherein each active pixel is an element of scalar measurement data comprising a binary-valued numerical value, the method comprising:
determining a cumulative sum of the square of row indices of active pixels, wherein an active pixel is defined as a measurement data element within the binary-valued image data having a specified binary numerical value;
determining a cumulative sum of the square of column indices of active pixels;
determining a cumulative sum of the product of row and column indices of active pixels;
determining a value according to a closed form algebraic formula comprising the cumulative sum of the square of row indices, the cumulative sum of the square of column indices, and the cumulative sum of the product of row and column indices;
determining the computed yaw angle of the oblong shape of binary-valued image data according to the value using an inverse trigonometric function operation; and
providing the computer yaw angle as an output for use by additional software.
2. The method of claim 1 wherein the additional software provides a user interface function.
3. The method of claim 2 wherein the computed yaw angle is used as a user interface quantity for controlling at least one aspect of a computer application.
4. The method of claim 1 wherein the binary-valued image data is produced from measurement data provided by a tactile sensor array.
5. The method of claim 4 wherein the tactile sensor array comprises a tactile proximity sensor.
6. The method of claim 4 wherein the tactile sensor array comprises a tactile pressure sensor.
7. The method of claim 4 wherein the binary-valued image data is produced at least in part responsive to contact of a human hand with the tactile sensor array.
8. The method of claim 4 wherein the binary-valued image data is produced by comparing each element of scalar measurement data to a selected numerical value, and if the value of the scalar measurement data is at least as large as the selected numerical value, assigning the specified binary numerical value to the associated pixel of the binary-valued image data.
9. The method of claim 1 wherein the inverse trigonometric function operation comprises an inverse cotangent function.
10. The method of claim 1 wherein the processor comprises an embedded controller.