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

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.