3jL SrSSKrSSKJrJrJr SSKrSSKJrJ r SSK J r J r SSK JrJr SSKJr S.S\R$S \S \\R$\R$44S jjrS.S \R$S \S \R$4S jjrS\R$S \R$4SjrS\R$4SjrS/S\R$S \S \R$4Sjjr\R2R4S/S\R$S \S \R$4Sjj5r\R2R4S\R$S\R$S \R$4Sj5r\R2R4S0S\R$S\R$S\\R$S\S \R$4 Sjj5rS1S\R$S\R$S\\R$S\SS \R$4 SjjrS\R$S\R$S \R$4S jr S!\R$S\R$S \R$4S"jr!S#\R$S$\R$S%\R$S \R$4S&jr"S'\R$S(\R$S)\R$S \R$4S*jr#S+\R$S,\R$S \R$4S-jr$g)2zKModule containing the functionalities for computing the Fundamental Matrix.N)LiteralOptionalTuple)KORNIA_CHECK_SAME_SHAPEKORNIA_CHECK_SHAPE)_torch_svd_castsafe_inverse_with_mask)convert_points_from_homogeneousconvert_points_to_homogeneous) solve_cubicpointsepsreturnc*URS:wa[UR5eURSS:wa[UR5eURup#nURURpeUR SSS9nX- nUR SSS9R SS9n [R"S 5X-- n XRUSS5-n [R"USS4XVS 9n XS 'XS 'U *US -U S 'U *US-U S'SU S'X4$)aNormalize points (isotropic). Computes the transformation matrix such that the two principal moments of the set of points are equal to unity, forming an approximately symmetric circular cloud of points of radius 1 about the origin. Reference: Hartley/Zisserman 4.4.4 pag.107 This operation is an essential step before applying the DLT algorithm in order to consider the result as optimal. Args: points: Tensor containing the points to be normalized with shape :math:`(B, N, 2)`. eps: epsilon value to avoid numerical instabilities. Returns: tuple containing the normalized points in the shape :math:`(B, N, 2)` and the transformation matrix in the shape :math:`(B, 3, 3)`. T)dimkeepdim)rprg@devicedtype).rr).rr).rr).rr).rr?).rr) ndimAssertionErrorshaperrmeannormmathsqrtviewtorchzeros) r rB_N_rrx_meancentered mean_radiusscale points_norm transforms ^/home/wildlama/miniconda3/lib/python3.13/site-packages/kornia/geometry/epipolar/fundamental.pynormalize_pointsr1s-&{{aV\\** ||B1V\\**||HA1MM6<r2points1points2c [U/SQ5 [U/SQ5 URSnURnURn[ U5upV[ U5upx[ R "USSS9up[ R "USSS9up[ R"U 5n [ R"X-X-XU -X-XX/ SS9n[[U55unn[U5n[U5n[ R"US4X4S9n[ RRU5n[ RRU5n[U5unn[U5unnUUS S 2S4'[ R "S UU-5U-US S 2S 4'[ R "S UU-5U-US S 2S4'UUS S 2S 4'[#U5n[ R$"US S9nUS :US :-nUR'5n[ R"U5nUS S 2SS4R)S 5nUS S 2SS4R)S 5nUU-U-n[+US 5)n[ R,"USU- U5n [ R,"UUU -U5n!U nU!nUR)S 5R/US S S 5n"UR)S 5R/US S S 5n#U"US S 2S S 2S S 4-U#US S 2S S 2S S 4--n$[ R,"U[ R"UUS9[ R0"UUS95n%U%U$S S 2S S 2SS4'[ R,"UR3US S S 5U$[ R0"U$55n$UR)S 5R5SS5U$-UR)S 5-n$[7U$5$)aCompute the fundamental matrix using the 7-point algorithm. The 7-point algorithm computes the fundamental matrix from exactly 7 point correspondences. Unlike the 8-point algorithm, this method can return up to 3 possible fundamental matrices as solutions to the rank-2 constraint, which is formulated as a cubic equation. Reference: Hartley/Zisserman 11.1.2 pag.281 Args: points1: A set of 7 points in the first image with shape :math:`(B, 7, 2)`. points2: A set of 7 points in the second image with shape :math:`(B, 7, 2)`. Returns: The computed fundamental matrices with shape :math:`(B, 3, 3, 3)`, containing up to 3 candidate solutions per batch. Invalid solutions are zeroed out. )r'72rrrrchunksrrNzbii->brr-q=r)rr<)rrrrr1r%chunk ones_likecatrJrErOr&r>detr einsumr count_nonzeroclone unsqueezerRr6expand zeros_liker$r=r9)&rSrTr'rr points1_norm transform1 points2_norm transform2x1y1x2y2onesXf1f2coeffsf1_detf2_detinv_f1r)inv_f2rootscnzvalid_root_mask_lambda_muf1_22f2_22_s_s_non_zero_maskmu_newlam_new f1_expanded f2_expandedfmatrixf22s& r0 run_7pointrs&w0w0 aA ^^F MME/8L/8L [[2a 8FB [[2a 8FB ??2 D  27BGRb"'22LRTUA""5a"8 9FB b B b B[[!Q Compute the fundamental matrix using (weighted) 8-point DLT, optimized. Args: points1: (B, N, 2), N >= 8 points2: (B, N, 2), N >= 8 weights: optional (B, N) nonnegative weights use_einsum_at_more_than_points: threshold for using einsum vs GEMM for large N Returns: (B, 3, 3) fundamental matrices )r'rDrWrNr'rDrrrXrr<z bni,bnj->bijrzbni,bnj,bn->bijrGr.)rrrrr1r%r\r]r^squeezer= contiguousr`rMrcr#r>r?r$rre diag_embedmHr9)rSrTrrpts1nT1pts2nT2rjrkrlrmrnr:r'rDr)r3wAwrBrChF_hatUSVS_newF_rank2rKs r0 run_8pointrsd$w0w0G-}}Q!W]]++7S#J/ == w}}Q/ / / /!)IE )IE [[Bq 1FB [[Bq 1FB ??2 D  27BGRb"'22LRTU]]^`aAggGA! - B#..014A ^Q2A   a  -Q[[_))++B R$//1B6A .a8ALL%%a(MFE f A FF1aOEe$GAq!   Q ESbSkE#ss(O%""5))ADD0G R" -A #A &&r2method)8POINT7POINTcUR5S:Xa [X5nU$UR5S:Xa[XU5nU$[SUS35e)afFind the fundamental matrix. Args: points1: A set of points in the first image with a tensor shape :math:`(B, N, 2), N>=8`. points2: A set of points in the second image with a tensor shape :math:`(B, N, 2), N>=8`. weights: Tensor containing the weights per point correspondence with a shape of :math:`(B, N)`. method: The method to use for computing the fundamental matrix. Supported methods are "7POINT" and "8POINT". Returns: the computed fundamental matrix with shape :math:`(B, 3*m, 3)`, where `m` number of fundamental matrix. Raises: ValueError: If an invalid method is provided. rrzInvalid method: z.. Supported methods are '7POINT' and '8POINT'.)upperrr ValueError)rSrTrrresults r0find_fundamentalrMs^*||~!G- M 8 #Gg6 M+F83abccr2F_matc6[U/SQ5 URSS:Xa [U5nO+URSS:XaUnO[UR5e[U/SQ5 [R "USSS9n[R "X-SSS9up4nX3-XD--n[R"US :S [R"U5- [R"U55n[R"X6-XF-XV-/SS 9n[R "USSS9$) aCompute the corresponding epipolar line for a given set of points. Args: points: tensor containing the set of points to project in the shape of :math:`(*, N, 2)` or :math:`(*, N, 3)`. F_mat: the fundamental to use for projection the points in the shape of :math:`(*, 3, 3)`. Returns: a tensor with shape :math:`(*, N, 3)` containing a vector of the epipolar lines corresponding to the points to the other image. Each line is described as :math:`ax + by + c = 0` and encoding the vectors as :math:`(a, b, c)`. )*rDDIMrrrr3rr<)dim0dim1rXgrr) rrr rr%r=r\r6r#r]r^)r rpoints_habcnulines r0compute_correspond_epilinesrksv01 ||B1!>v!F b Q V\\**uo.xbr:Hkk%*1=GA!uqu}B R#XsUZZ^3U__R5H IB 99afafaf-2 6D ??4br 22r2linesc[U/SQ5 [U/SQ5 URSS:Xa [U5nO+URSS:XaUnO[UR5eU[R "/SQUR URS9RSSS5-n[RRX#SS9nU$) aCompute the perpendicular to a line, through the point. Args: lines: tensor containing the set of lines :math:`(*, N, 3)`. points: tensor containing the set of points :math:`(*, N, 2)`. Returns: a tensor with shape :math:`(*, N, 3)` containing a vector of the epipolar perpendicular lines. Each line is described as :math:`ax + by + c = 0` and encoding the vectors as :math:`(a, b, c)`. )rrDr)rrDtworr)rrr)rrrr) rrr rr%tensorrrr$r>cross)rr rinfinity_pointperps r0get_perpendicularrsuo.v01 ||A!!>v!F aA V\\**U\\)5;;u||\aabcefhijjN++H!+LD Kr2pts1pts2Fmc[U[R5(d[S[ U535e[ UR 5S:dUR SSS:Xd[SUR 35eUR SS:Xa [U5nUR SS:Xa [U5n[X5n[X15n[[RRX4SS 95nU$) a4Return closest point on the epipolar line to the correspondence, given the fundamental matrix. Args: pts1: correspondences from the left images with shape :math:`(*, N, (2|3))`. If they are not homogeneous, converted automatically. pts2: correspondences from the right images with shape :math:`(*, N, (2|3))`. If they are not homogeneous, converted automatically. Fm: Fundamental matrices with shape :math:`(*, 3, 3)`. Called Fm to avoid ambiguity with torch.nn.functional. Returns: point on epipolar line :math:`(*, N, 2)`. z#Fm type is not a torch.Tensor. Got rr<N)rrz#Fm must be a (*, 3, 3) tensor. Got rrr) isinstancer%Tensor TypeErrortyper5rrr rrr r>r)rrrline1in2r points1_in_2s r0"get_closest_point_on_epipolar_liners b%,, ' '=d2hZHII BHH "((23-6"9>rxxjIJJ zz"~,T2 zz"~,T2*44H X ,D25<<3E3EhZ[3E3\]L r2E_matK1K2cp[U/SQ5 [U/SQ5 [U/SQ5 [URSS5[URSS5s=:Xa"[URSS5:Xd[e [e[ U5SR SS5U-[ U5S-$)aGet the Fundamental matrix from Essential and camera matrices. Uses the method from Hartley/Zisserman 9.6 pag 257 (formula 9.12). Args: E_mat: The essential matrix with shape of :math:`(*, 3, 3)`. K1: The camera matrix from first camera with shape :math:`(*, 3, 3)`. K2: The camera matrix from second camera with shape :math:`(*, 3, 3)`. Returns: The fundamental matrix with shape :math:`(*, 3, 3)`. rNr<rr)rr5rrr r=)rrrs r0fundamental_from_essentialrsuo.r?+r?+ u{{3B C" $6 L#bhhsm:L L M "2 &q ) 4 4R UR[R 5nUR[R 5nUSS S2SS24nU"USS S 2SS24USS S 2SS245nUSSS 2SS24nUSS S2SS24nU"USS S 2SS24USS S 2SS245nUSSS 2SS24n U"XG5U"XW5U"Xg5pn U"XH5U"XX5U"Xh5pn U"XI5U"XY5U"Xi5nnn[R"U R5RS S 5U R5RS S 5U R5RS S 5U R5RS S 5UR5RS S 5UR5RS S 5UR5RS S 5UR5RS S 5UR5RS S 5/ S S9nUR"/URSSQS PS P76RU5$)aGet the Fundamental matrix from Projection matrices. Args: P1: The projection matrix from first camera with shape :math:`(*, 3, 4)`. P2: The projection matrix from second camera with shape :math:`(*, 3, 4)`. Returns: The fundamental matrix with shape :math:`(*, 3, 3)`. )rr4Nr<rPyrc.[R"X/SS9$)Nr<r)r%r^)rPrs r0vstack,fundamental_from_projections..vstacksyy!R((r2.rrrrrr) rrrr%rrfloat32float64tor^r_reshaper$)rrr input_dtypeX1X2X3Y1Y2Y3X1Y1X2Y1X3Y1X1Y2X2Y2X3Y2X1Y3X2Y3X3Y3F_vecs r0fundamental_from_projectionsrsr?+r?+ xx}" %)%,,)5<<)ELL)((K5==%--88 UU5== ! UU5== ! CQJB 3!Q;C1aK 1B C!QJB CQJB 3!Q;C1aK 1B C!QJBb~vb~vb~Db~vb~vb~Db~vb~vb~$D II HHJ  r1 % HHJ  r1 % HHJ  r1 % HHJ  r1 % HHJ  r1 % HHJ  r1 % HHJ  r1 % HHJ  r1 % HHJ  r1 %   E :: +rxx} +a + + . .{ ;;r2)g:0yE>)r[)Ni)Nr)%__doc__r"typingrrrr%kornia.core.checkrrkornia.core.utilsrr kornia.geometry.conversionsr r kornia.geometry.solversr rfloatr1r9rErJrOjitscriptrRrintrrrrrrrr2r0rs$R ++ IEf/3"U\\3"3"u||UZUaUaGaAb3"lF F5FELLF(  5<<  ELL  ELL  ELL u   Eell b- b-u||b- b-b-J'+*- F' \\F' \\F'ell #F'%( F'  \\ F'F'X'+*2  \\ \\ell # & '   \\ <3 3U\\3ell3BU\\5<<ELL4U\\SXS_S_didpdp:gellg g%,,g[`[g[gg82