Patent ID: 8306361

Claim:
A method for restoring a three-dimensional image from a plurality of two-dimensional images of an object, the method comprising the steps of: extracting coordinates d ij (x ij , y ij ) of feature points i (i=1, . . . , n, where n is an integer greater than or equal to 2) in two-dimensional images j (j=1, . . . , m, where m is an integer greater than or equal to 3); and computing three-dimensional coordinates s i (X i , Y i , Z i ) of the feature points and a matrix M representing a transformation from two-dimensional coordinates to three-dimensional coordinates based on the two-dimensional coordinates d ij (x ij , y ij ) of the feature points, wherein the step of computing three-dimensional coordinates s i (X i , Y i , Z i ) of the feature points and a matrix M representing a transformation from two-dimensional coordinates to three-dimensional coordinates includes the steps of: performing an upper bidiagonalization on a matrix D so as to obtain an upper bidiagonal matrix B of the matrix D, the matrix D being defined as D = [ x 1 1 … x i 1 … x n 1 … … … … … x 1 j … x i j … x n j … … … … … x 1 m … x i m … x n m y 1 1 … y i 1 … y n 1 … … … … … y 1 j … y i j … y n j … … … … … y 1 m … y i m … y n m ] ; [ Expression ⁢ ⁢ 1 ] obtaining singular values σ j (σ 1 ≧σ 2 ≧ . . . ≧σ r >0, where r is equal to a rank of the matrix D) of the matrix B as singular values of the matrix D; obtaining singular vectors of the matrix D for σ 1 , σ 2 and σ 3 ; computing a matrix E satisfying E=CC T for a matrix C such that M=M′C, where M′=L′ (Σ′) 1/2 , Σ′ is a 3×3 matrix having σ 1 , σ 2 and σ 3 as diagonal elements and the other elements being 0, and L′ is a matrix having singular vectors of the matrix D corresponding to σ 1 , σ 2 and σ 3 arranged from a left side in this order; computing the matrix C from the matrix E; and computing the three-dimensional coordinates s i (X i , Y i , Z i ) and the matrix M representing the transformation from the matrix C, wherein the step of obtaining singular vectors of the matrix D for σ 1 , σ 2 and σ 3 includes a step of performing a Twisted decomposition on a matrix B T B−σ j 2 I by using a Miura inverse transformation, an sdLVvs transformation, an rdLVvs transformation and a Miura transformation so as to diagonalize a matrix B T B, where I is a unit matrix.