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A class that creates a trifocal tensor from either a pair of camera matrices or three corresponding point sets. <code>Trifocal( Pi, Pii )</code> <code>Trifocal( x0, x1, x2 )</code> Includes methods for testing constraints, retrieving epipoles and fundamental matrices.

Python, 178 lines
 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 from numpy import * import cv2 class Trifocal: def __init__(self, *args): '''Initialize with a set of 2 or 3 camera projection matrices (3x4 or 4x4) or with 3 sets of corresponding points (all 3xN).''' if args.shape == (3,4) or args.shape == (4,4): self.T, self.scale = self.tensor_P( list(args) ) elif len(args) == 3 and args.shape == 3: self.T, self.scale = self.tensor_pts( *args ) else: raise Warning, 'Trifocal initialization failed!' def __call__(self, A, B, transpose=False): '''Method to pre and post multiply matrices to the tensor.''' if A == None: A = 1. if B == None: B = 1. return r_[[dot(dot(A,self.T[i]),B) for i in (0,1,2)]] def __str__(self): return str(self.T) # CONSTRAINT TESTING METHODS def lll(self, line1, line2, line3): return dot(self._ll(line2,line3), skew(line1)) def pll(self, pt1, line2, line3): xT = sum([pt1[i]*self.T[i] for i in (0,1,2)],0) return dot(dot(line2,xT),line3) def plp(self, pt1, line2, pt3): xT = sum([pt1[i]*self.T[i] for i in (0,1,2)],0) return dot(dot(line2,xT),skew(pt3)) def ppl(self, pt1, pt2, line3): xT = sum([pt1[i]*self.T[i] for i in (0,1,2)],0) return dot(dot(skew(pt2),xT),line3) def ppp(self, pt1, pt2, pt3): xT = sum([pt1[i]*self.T[i] for i in (0,1,2)],0) return dot(dot(skew(pt2),xT),skew(pt3)) # LINE TRANSFER METHOD def _ll(self, line2, line3): '''Calculate point in 1st image from lines in 2nd and 3rd.''' return r_[[dot(dot(line2,self.T[i]),line3) for i in (0,1,2)]] # POINT TRANSFER METHODS def p_l(self, pt1, line3): '''Calculate point in 2nd image from point in 1st and line in 3rd.''' xT = sum([pt1[i]*self.T[i] for i in (0,1,2)],0) return dot(xT,line3) def pl_(self, pt1, line2): '''Calculate point in 3rd image from point in 1st and line in 2rd.''' xT = sum([pt1[i]*self.T[i] for i in (0,1,2)],0) return dot(line2,xT) def getEpipoles(self): '''Returns the epipole/position of camera 1 in image 2 and 3.''' u = r_[[cv2.SVDecomp(t.T)[-1] for t in self.T]] ei = cv2.SVDecomp(u)[-1] v = r_[[cv2.SVDecomp(t)[-1] for t in self.T]] eii = cv2.SVDecomp(v)[-1] return ei, eii def getFundamentalMat(self): '''Returns the f-mat of camera 2 to 1 and camera 3 to 1.''' ei,eii = self.getEpipoles() F21 = array([dot(dot(skew(ei),t),eii) for t in self.T]).T F31 = array([dot(dot(skew(eii),t.T),ei) for t in self.T]).T return F21, F31 def getProjectionMat(self, from_E=True): ei,eii = self.getEpipoles() ei = cv2.normalize(ei).flatten() eii = cv2.normalize(eii).flatten() if from_E == True: F21,F31 = self.getFundamentalMat() H21 = H_from_E(F21) H31 = H_from_E(F31) v1 = r_[0.5,0.5,50,1.] v2 = r_[1.,1.,51,1.] for H in H21: ln2 = cross(dot(H,v1)[:3],dot(H,v2)[:3]) pt3 = self.pl_(v1[:3]/v1, ln2) pt3 /= pt3 print pt3 for H2 in H31: print dot(H2,v1)[:3]/dot(H2,v1)[:3] return H21,H31 else: Pi = eye(4) Pi[:3,:3] = array([dot(t,eii) for t in self.T]).T Pi[:3,3] = ei # K = cv2.decomposeProjectionMatrix(Pi[:3]) # Pi[:3] = dot(cv2.invert(K),Pi[:3]) return Pi def tensor_pts(self, x0, x1, x2): '''Calculates tensor from point correspondences.''' N = len(x0) M = zeros((N*4,27)) for i in range(N): for j in range(3): block = zeros((4,9)) block[[0,1,0,1,2,3,2,3,0,2,1,3,0,1,2,3], [0,1,2,2,3,4,5,5,6,6,7,7,8,8,8,8]] = x0[j,i] block[:2,6:] *= -x1[0,i] block[2:,6:] *= -x1[1,i] block[:2,2] *= -x2[:2,i] block[2:,5] *= -x2[:2,i] block[:2,8] *= -x2[:2,i] block[2:,8] *= -x2[:2,i] M[i*4:i*4+4, j*9:j*9+9] = block.copy() V = cv2.SVDecomp(M) self.T = V[-1,:27].reshape((3,3,3)) return self.T, 1.0 def tensor_P(self, Plist): '''Calculates tensor from two camera projections. Plist is a list of 3x4 projections. If three are listed then the first is assumed to be the origin and not considered. If two are listed then it is assumed that the origin projection was omitted.''' try: if len(Plist) == 3: A = Plist[:3] B = Plist[:3] else: A = Plist[:3] B = Plist[:3] except: raise Warning, 'List of two or three 3x4 (or 4x4) projection matrices.' T = zeros((3,3,3)) for i in range(3): for j in range(3): for k in range(3): T[i,j,k] = A[j,i]*B[k,3] - A[j,3]*B[k,i] scale = sqrt(sum(B[:3,3]**2))/sqrt(sum(A[:3,3]**2)) return T, scale def skew(v): if len(v) == 4: v = v[:3]/v skv = roll(roll(diag(v.flatten()), 1, 1), -1, 0) return skv - skv.T def H_from_E(E, RandT=False): '''Returns a 4x4x4 matrix of possible H translations. Or returns the two rotations and translation vectors when keyword is True. ''' S,U,V = cv2.SVDecomp(E) #TIP: Recover E by dot(U,dot(diag(S.flatten()),V)) W = array([[0,-1,0],[1,0,0],[0,0,1]]) R1 = dot(dot(U,W),V) R2 = dot(dot(U,W.T),V) if cv2.determinant(R1) < 0: R1,R2 = -R1,-R2 t1 = U[:,2] t2 = -t1 if RandT: return R1, R2, t1, t2 H = zeros((4,4,4)) H[:2,:3,:3] = R1 H[2:,:3,:3] = R2 H[[0,2],:3,3] = t1 H[[1,3],:3,3] = t2 H[:,3,3] = 1 return H

The estimation of the tensor from points uses equation 16.2 in Hartley/Zimmerman. The version only covers algorithm 15.1 (i and ii) and 16.2 up to (iii). P' and P'' can be calculated from the fundamental matrices and use triangulation to get the relative scale between the two. Created by J W J on Tue, 28 Aug 2012 (MIT)