Method and computations for calculating an optical axis vector of an imaged eye

A computing device, comprising:

• a digital camera;
• and
• a processor coupled to the camera and configured with processor-executable instructions to perform operations comprising:
• obtaining a digital image of an eye with the digital camera;
• processing the digital image to determine an optical axis vector of the eye in a three-axis coordinate system comprising X, Y and Z axes, wherein the processing comprises:
• determining an ellipse equation defining an iris disc corresponding to the eye, on an XY plane of the three-axis coordinate system;
• deriving a set of equations based on the ellipse equation corresponding to a plurality of edge points of the iris disc in the three-axis coordinate system;
• and
• iteratively calculating an estimated iris diameter until a difference between the estimated iris diameter and a predetermined iris diameter is less than a threshold, comprising:
• estimating a ray length from a spatial origin of the three-axis coordinate system to a first edge point of the plurality of edge points;
• solving the set of equations based on the estimated ray length to calculate a plurality of solutions;
• calculating the estimated iris diameter based on the solutions;
• and
• calculating an optical axis vector of the eye in the three-axis coordinate system based on the solutions,
• wherein the solutions comprise a first solution and a second solution based on two sets of the edge points, respectively, and
• wherein calculating the optical axis vector comprises:
• calculating a first optical axis vector based on the first solution, calculating a second optical axis vector based on the second solution;
• and
• generating a composite optical axis vector based on the first optical axis vector and the second optical axis vector.

A computing device, comprising:

• means for obtaining a digital image of an eye;
• and
• means for processing the digital image to determine an optical axis vector of the eye in a three-axis coordinate system comprising X, Y and Z axes, wherein the means for processing comprises:
• means for determining an ellipse equation defining an iris disc corresponding to the eye, on an XY plane of the three-axis coordinate system;
• mean for deriving a set of equations based on the ellipse equation corresponding to a plurality of edge points of the iris disc in the three-axis coordinate system;
• and
• means for iteratively calculating an estimated iris diameter until a difference between the estimated iris diameter and a predetermined iris diameter is less than a threshold, comprising:
• means for estimating a ray length from a spatial origin of the three-axis coordinate system to a first edge point of the plurality of edge points;
• means for solving the set of equations based on the estimated ray length to calculate a plurality of solutions;
• means for calculating the estimated iris diameter based on the solutions;
• and
• means for calculating an optical axis vector of the eye in the three-axis coordinate system based on the solutions,
• wherein the solutions comprise a first solution and a second solution based on two sets of the edge points, respectively, and
• wherein the means for calculating the optical axis vector comprises:
• means for calculating a first optical axis vector based on the first solution,
• means for calculating a second optical axis vector based on the second solution;
• and
• means for generating a composite optical axis vector based on the first optical axis vector and the second optical axis vector.

A non-transitory processor-readable storage medium having stored thereon processor-executable instructions configured to cause a processor of a computing device including a digital camera to perform operations comprising:

• obtaining a digital image of an eye with the digital camera;
• and
• processing the digital image to determine an optical axis vector of the eye in a three-axis coordinate system comprising X, Y and Z axes, wherein the processing comprises:
• determining an ellipse equation defining an iris disc corresponding to the eye, on an XY plane of the three-axis coordinate system;
• deriving a set of equations based on the ellipse equation corresponding to a plurality of edge points of the iris disc in the three-axis coordinate system;
• and
• iteratively calculating an estimated iris diameter until a difference between the estimated iris diameter and a predetermined iris diameter is less than a threshold, comprising:
• estimating a ray length from a spatial origin of the three-axis coordinate system to a first edge point of the plurality of edge points;
• solving the set of equations based on the estimated ray length to calculate a plurality of solutions;
• calculating the estimated iris diameter based on the solutions;
• and
• calculating an optical axis vector of the eye in the three-axis coordinate system based on the solutions,
• wherein the solutions comprise a first solution and a second solution based on two sets of the edge points, respectively, and
• wherein calculating the optical axis vector comprises:
• calculating a first optical axis vector based on the first solution,
• calculating a second optical axis vector based on the second solution;
• and
• generating a composite optical axis vector based on the first optical axis vector and the second optical axis vector.