Patent ID: 8055074

Claim:
A method of approximating an iris boundary, comprising the steps of: acquiring an image of an eye, including an iris boundary; noting a plurality of unequally spaced boundary points on the boundary; selecting a fixed reference point; generating an approximate boundary representation comprising a least squares approximation by a Fourier Series as a function of angle θ i about said fixed point of the distance of said boundary points in the image from said fixed point; and the spaced boundary points being not all equally spaced in θ i , and in which said least-squares approximation minimizes the sum of squares of errors in the distances taken over the boundary points, the approximate boundary representation being generated by numerically solving the system of linear equations PV=C or a mathematical equivalent thereof, for the unknown matrix V, where: V = [ a 0 a 1 ⋮ a N b 1 ⋮ b N ] ⁢ ⁢ C = [ C 0 C 1 ⋮ C N C N + 1 ⋮ C 2 ⁢ N ] with ⁢ ⁢ C 0 = ∑ i = 0 M ⁢ r i , ⁢ C k = ∑ i = 0 M ⁢ r i ⁢ cos ⁢ ⁢ k ⁢ ⁢ θ i ⁢ ⁢ and ⁢ ⁢ C N + k = ∑ i = 0 M ⁢ r i ⁢ sin ⁢ ⁢ k ⁢ ⁢ θ i ⁢ ⁢ for ⁢ ⁢ k = 1 ⁢ ⁢ … ⁢ ⁢ N , and ⁢ ⁢ where ⁢ ⁢ P ⁢ ⁢ is ⁢ ⁢ a ⁢ ⁢ 2 ⁢ n + 1 ⁢ ⁢ by ⁢ ⁢ 2 ⁢ N = 1 ⁢ ⁢ matrix ⁢ ⁢ given ⁢ ⁢ by : P k , n = ∑ i = 1 M ⁢ cos ⁢ ⁢ n ⁢ ⁢ θ i ⁢ cos ⁢ ⁢ k ⁢ ⁢ θ i ⁢ ⁢ for ⁢ ⁢ k = 0 ⁢ ⁢ … ⁢ ⁢ N ⁢ ⁢ and ⁢ ⁢ n = 0 ⁢ ⁢ … ⁢ ⁢ N ⁢ ⁢ ( Upper ⁢ ⁢ Left ⁢ ⁢ Matrix ) P k , N + n = ∑ i = 1 M ⁢ sin ⁢ ⁢ n ⁢ ⁢ θ i ⁢ cos ⁢ ⁢ k ⁢ ⁢ θ i ⁢ ⁢ for ⁢ ⁢ k = 0 ⁢ ⁢ … ⁢ ⁢ N ⁢ ⁢ and ⁢ ⁢ ⁢ n = 1 ⁢ ⁢ … ⁢ ⁢ N ⁢ ⁢ ( Upper ⁢ ⁢ Right ⁢ ⁢ Matrix ) P N + k , n = ∑ i = 1 M ⁢ cos ⁢ ⁢ n ⁢ ⁢ θ i ⁢ sin ⁢ ⁢ k ⁢ ⁢ θ i ⁢ ⁢ for ⁢ ⁢ k = 1 ⁢ ⁢ … ⁢ ⁢ N ⁢ ⁢ and ⁢ ⁢ n = 0 ⁢ ⁢ … ⁢ ⁢ N ⁢ ⁢ ( Lower ⁢ ⁢ Left ⁢ ⁢ Matrix ) P N + k , N + n = ∑ i = 1 M ⁢ sin ⁢ ⁢ n ⁢ ⁢ θ i ⁢ sin ⁢ ⁢ k ⁢ ⁢ θ i ⁢ ⁢ for ⁢ ⁢ k = 1 ⁢ ⁢ … ⁢ ⁢ N ⁢ ⁢ and ⁢ ⁢ n = 1 ⁢ ⁢ … ⁢ ⁢ N ⁢ ⁢ ( Lower ⁢ ⁢ Right ⁢ ⁢ Matrix ) .