High-performance closed-form single-scan calculation of oblong-shape rotation angles from binary images of arbitrary size and location using running sums

A computer implemented data processing system comprising:

• a memory that stores binary-valued image data;
• and
• a processor in communication with the memory that:
• receives the binary-valued image data, the binary-valued image comprising an array of pixels having rows and columns wherein each row and column has a unique associated index value, and each pixel having has a unique row index value and column index value wherein each pixel further comprises a binary value defined as a scalar measurement, the binary-valued image data comprising a subset of pixels arranged to form an oblong shape within the image data;
• computes the geometric center of the oblong shape, the geometric center comprising a row center value and a column center value;
• defines a corresponding centered row index value by subtracting the row center value from the row index value for each row index value;
• defines a corresponding centered column index value by subtracting the column center value from the column index value for each column index value;
• defines an active pixel as a measurement data element within the binary-valued image data exceeding a specified value;
• computes a first cumulative sum of the square of centered row index values of active pixels, second cumulative sum of the square of centered column index values of active pixels, and a third cumulative sum of the product of centered row index values and centered column index values of active pixels;
• computes one or more numerical quantities within a closed form algebraic formula for a ratio of two terms of an inertial matrix defined by the binary-valued image data using each of first, second, and third cumulative sums;
• transforms the ratio into a calculated numerical angle value using an inverse trigonometric function operation;
• and provides the calculated numerical angle value to additional software.