o oi[@sndZddlmZmZddlZddlmZmZmZm Z m Z ddl m Z m Z mZddlmZddlmZmZddlmZmZd d lmZmZd d lmZmZd d lmZgd Zd:dej dej deej dej fddZ!d;dej de"de"de"dej f ddZ#dej de"dej fddZ$dej d ej d!ej dej fd"d#Z%d$ej deej ej ej ffd%d&Z&d$ej deej ej ej ffd'd(Z'd)ej d*ej d+ej d,ej dej f d-d.Z(d$ej deej ej ffd/d0Z) d:d$ej d ej d!ej d1ej d2ej d3eej deej ej ej ffd4d5Z*d)ej d*ej d+ej d,ej deej ej ff d6d7Z+ d:dej dej deej dej fd8d9Z,dS)=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)`. Returns: the computed essential matrix with shape :math:`(B, 3, 3)`. )BN2rzNumber of points should be >=5Nr)dimchunksr)) r r r shapetorchchunkrcat transpose diag_embednull_to_Nister_solution) rr r! batch_size_x1y1x2y2onesXw_diagE_Nisterr>V/home/ubuntu/.local/lib/python3.10/site-packages/kornia/geometry/epipolar/essential.py run_5point.s   0  r@null_matijratiocCs|dd|||fSNr>)rBrCrDrEr>r>r? fun_select[srGr;r4c% Cs t|\}}}|ddddddf}|ddddddddf}t|dd|j|jd}t|d|j|jd}ttt|d d t|d d tt|d d t|d d t|d d ttt|d d t|d d tt|d d t|d d t|d d ttt|d d t|d d tt|d d t|d d t|d d |ddd f<t gd gdgdg}t dD]E} t dD]>} tt|| d t|| d tt|| d t|| d tt|| d t|| d |dd|| | f|| | fdf<qqt dD]Y} d|dd|d| f|dd|d| f|dd|d| f} |dd|d| f| 8<|dd|d| f| 8<|dd|d| f| 8<qd } t dD]k} t dD]c} t|dd|| d f|| d fdft|d | t|dd|| d f|| d fdft|d | t|dd|| d f|| d fdft|d | } | |dd| f<| d 7} qnqh|ddddddf}t j |ddddddft t j |tt j |ddddddfdk}|d kr*t jd|j|jdd|dddSt||ddddf||}t j||ddddf|fdd}|jd }t|jd dd|j|jd}t dD]} d|dd| d f<|dddd | dd | ddf|dd| | d d df<|dd| | d d df|dddd | dd | ddf8<d|dd| df<|dddd | dd | ddf|dd| | d ddf<|dd| | d ddf|dddd | dd | ddf8<d|dd| df<|dddd | dd | ddf|dd| | d d df<|dd| | d ddf|dddd | dd | ddf8<qct|}t|ddf|j|jd}t|d d dd dfjd |j|jd}||ddd dd df<|dddfd}t |d kt j d |jd!|}|ddddf ||dddddf<t t j |}|d }t|dddddd f|d|ddddd d f||ddd dd df||ddd dddf|ddd dddf|d|ddd dddf||ddd dddf||ddd dddffd d}|d d}|ddd ddd f|d|ddd dd df|d|ddd ddd"f||ddd dd"df||ddd dddfd d d}t t j |ddddd d d d f|ddddd d f}t |ddd fd ||ddd fd d#k!}t t |ddddd ddfd ||ddddd ddfd d#k}|"d"d }t #|r?t j $||\}}t j %|t |dd||} | ||<||}!|!ddd d f|ddddd f |!ddd d f|ddddd f |!ddd df|d|!ddddf}"d$t &|ddddd f d |ddddd f d |dd d$}#|"|#9}"|"'|ddddd}"t jd|"j|"jdd|ddd}$|"|$|<|$S)%a;Use Nister's 5PC to solve essential matrix. The linear system is solved by Nister's 5-point algorithm [@nister2004efficient], and the solver implemented referred to [@barath2020magsac++][@wei2023generalized][@wang2023vggsfm]. Args: X: Coefficients for the null space :math:`(B, N, 2), N>=8`. batch_size: batcs size of the input, the number of image pairs :math:`B`. Returns: the computed essential matrix with shape :math:`(B, 3, 3)`. Note that the returned E matrices should be the same batch size with the input. Nr'r, devicedtype<rrr( )rrIrJ)rI()rJrQ2rA?)rr)rr)r(r()rMrLr+ r& g:0yE>)rM gMbP??)(rr1rrLrMr multiply_deg_two_one_polymultiply_deg_one_polyrGr.tensorrangelinalg matrix_rankmaxrsumrexpandclonerr0r-determinant_to_polynomial unsqueezerrealeigvalsrsquarematmulinvabsflattensqueezeanyqrsolvesqrtview)%r;r4r5Vnull_ nullSpacecoeffsdindicesrCrDtcntrowbsingular_filtereliminated_matcoeffs_batch_size_filteredAcsCeye_matcs_deroots roots_unsquBsbsxzsmaskq_batchr_batch xyz_to_feednullSpace_filteredEsrnE_returnr>r>r?r3_s"      ( L  $  666  $2( $  DLDLDP *,          F <R "**T(r3F_matK1K2cCs>t|gdt|gdt|gd|dd||S)aGet Essential matrix from Fundamental and Camera matrices. Uses the method from Hartley/Zisserman 9.6 pag 257 (formula 9.12). Args: F_mat: The fundamental 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 essential matrix with shape :math:`(*, 3, 3)`. *3rr,r'r r1)rrrr>r>r?rsrE_matc Cst|gdt|\}}}|dd}t|}|dddfd9<|dd}tt|dkd|||}tt|dkd|||}ttgd g |}|d d 7<|||}||dd|} |} | } |dddf} | | | fS) aDecompose an essential matrix to possible rotations and translation. This function decomposes the essential matrix E using svd decomposition [96] and give the possible solutions: :math:`R1, R2, t`. Args: E_mat: The essential matrix in the form of :math:`(*, 3, 3)`. Returns: A tuple containing the first and second possible rotation matrices and the translation vector. The shape of the tensors with be same input :math:`[(*, 3, 3), (*, 3, 3), (*, 3, 1)]`. rr,r'.NgrU).NN)rUrUr]).r(r(r]) r rr1rrr.detrr`type_as) rUr5rwVtrmasktWU_W_VtU_Wt_VtR1R2Tr>r>r?r-s     rc Cs\t|gdt|jdkr|ddd}|jd}|d|d|d}}}tdtj||dd dd d d}tj tj j ||dd tj j ||dd tj j ||dd gd d }tj |dd d}tj |d d }|ddddf||} |ddd| d} tj| d | dd } | tj | dd d} tj|ddf|j|jd} | dddf| ddd f| dddf}}}| || dddd f<| ddd df<|| | ddddf<| ddddf<| || ddd df<| dddd f<| }| }t|| || | d}t|||||d}||| dfS)a4Decompose the essential matrix to rotation and translation. Recover rotation and translation from essential matrices without SVD reference: Horn, Berthold KP. Recovering baseline and orientation from essential matrix[J]. J. Opt. Soc. Am, 1990, 110. Args: E_mat: The essential matrix in the form of :math:`(*, 3, 3)`. Returns: A tuple containing the first and second possible rotation matrices and the translation vector. The shape of the tensors with be same input :math:`[(*, 3, 3), (*, 3, 3), (*, 3, 1)]`. rrAr'r.r).r).r(rSr,)dim1dim2r+rTr)keepdimN)r)indexrKr()r lenr-rvr.rudiagonalr1rerrbcrossnormargmaxrirfsizegatherrqrrLrMr)rr#e1e2e3 scale_factorcross_productsnormslargeste_cross_productsindex_expandedb1b1_B1t0t1t2B2b2rrr>r>r?rXs4 ,24(((""rrrrrcCs^t|gdt|gdt|gdt|gdt||||\}}t|d}||S)aGet the Essential matrix from Camera motion (Rs and ts). Reference: Hartley/Zisserman 9.6 pag 257 (formula 9.12) Args: R1: The first camera rotation matrix with shape :math:`(*, 3, 3)`. t1: The first camera translation vector with shape :math:`(*, 3, 1)`. R2: The second camera rotation matrix with shape :math:`(*, 3, 3)`. t2: The second camera translation vector with shape :math:`(*, 3, 1)`. Returns: The Essential matrix with the shape :math:`(*, 3, 3)`. rrr1r)r rr)rrrrRr}Txr>r>r?rs rcCsPt|gdt|\}}}t||||gdd}t|| || gdd}||fS)aGet Motion (R's and t's ) from Essential matrix. Computes and return four possible poses exist for the decomposition of the Essential matrix. The possible solutions are :math:`[R1,t], [R1,-t], [R2,t], [R2,-t]`. Args: E_mat: The essential matrix in the form of :math:`(*, 3, 3)`. Returns: The rotation and translation containing the four possible combination for the retrieved motion. The tuple is as following :math:`[(*, 4, 3, 3), (*, 4, 3, 1)]`. rr+)r rr)rrrr}RsTsr>r>r?rs rr6r8rcCst|gdt|gdt|gdt|gdt|gdtt|jddt|jddkoBt|jddkn|dur]t|ddgt|j|jddkt|jdk}|r|d}|d}|d}|d}|d}|dur|d}t|\}}td |} td |} | dddfdd dd} | dddfdd dd} |dddfdd dd}t|| | } |} |} |dddfdd dd}t|| | }|dddfdd dd}|dddfdd dd}t | |||}t | | |}t | | |}|d k|d k@}|dur|| d M}t j |ddd dd }|dd|fddddf}|dd|fddddf}|dd|fddddf}|rf|d}|d}|d}|||fS)aRecover the relative camera rotation and the translation from an estimated essential matrix. The method checks the corresponding points in two images and also returns the triangulated 3d points. Internally uses :py:meth:`~kornia.geometry.epipolar.decompose_essential_matrix` and then chooses the best solution based on the combination that gives more 3d points in front of the camera plane from :py:meth:`~kornia.geometry.epipolar.triangulate_points`. Args: E_mat: The essential matrix in the form 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)`. x1: The set of points seen from the first camera frame in the camera plane coordinates with shape :math:`(*, N, 2)`. x2: The set of points seen from the first camera frame in the camera plane coordinates with shape :math:`(*, N, 2)`. mask: A boolean mask which can be used to exclude some points from choosing the best solution. This is useful for using this function with sets of points of different cardinality (for instance after filtering with RANSAC) while keeping batch semantics. Mask is of shape :math:`(*, N)`. Returns: The rotation and translation plus the 3d triangulated points. The tuple is as following :math:`[(*, 3, 3), (*, 3, 1), (*, N, 3)]`. r)rr$r%Nr,rr$r'r(rArVrUrTrr)r r rr-rr rrfrrrrir.rdre)rrrr6r8r unbatchedrtsrrP1rrP2r;d1d2 depth_mask mask_indicesR_outt_out points3d_outr>r>r?rs\!F         rcCs\t|gdt|gdt|gdt|gd||dd}|||}||fS)aCompute the relative camera motion between two cameras. Given the motion parameters of two cameras, computes the motion parameters of the second one assuming the first one to be at the origin. If :math:`T1` and :math:`T2` are the camera motions, the computed relative motion is :math:`T = T_{2}T^{-1}_{1}`. Args: R1: The first camera rotation matrix with shape :math:`(*, 3, 3)`. t1: The first camera translation vector with shape :math:`(*, 3, 1)`. R2: The second camera rotation matrix with shape :math:`(*, 3, 3)`. t2: The second camera translation vector with shape :math:`(*, 3, 1)`. Returns: A tuple with the relative rotation matrix and translation vector with the shape of :math:`[(*, 3, 3), (*, 3, 1)]`. rrr,r'r)rrrrrr}r>r>r?r=s rcCst||||j}|S)a{Find essential matrices. Args: points1: A set of points in the first image with a tensor shape :math:`(B, N, 2), N>=5`. points2: A set of points in the second image with a tensor shape :math:`(B, N, 2), N>=5`. weights: Tensor containing the weights per point correspondence with a shape of :math:`(5, N)`. Returns: the computed essential matrices with shape :math:`(B, 10, 3, 3)`. Note that all possible solutions are returned, i.e., 10 essential matrices for each image pair. To choose the best one out of 10, try to check the one with the lowest Sampson distance. )r@torM)rr r!Er>r>r?r_srrF)rA)-__doc__typingrrr. kornia.corerrrrrkornia.core.checkr r r kornia.geometryr kornia.utilsr rkornia.utils.helpersrrnumericrr projectionrr triangulationr__all__Tensorr@intrGr3rrrrrrrrr>r>r>r?st  ( $-";$$+(E   i #