o oiIC @sdZddlmZmZmZddlZddlmZmZm Z m Z m Z m Z ddl mZmZddlmZmZddlmZddlmZdd lmZmZd3d ed ed eeeffddZd3ded ed efddZdeded efddZd4dededeed efddZ d5dededeededd ef ddZd eded efd d!Z d"ed ed efd#d$Z!d%ed&ed'ed efd(d)Z"d*ed+ed,ed efd-d.Z#d/ed0ed efd1d2Z$dS)6zKModule containing the functionalities for computing the Fundamental Matrix.)LiteralOptionalTupleN)Tensor concatenate ones_likestackwherezeros)KORNIA_CHECK_SAME_SHAPEKORNIA_CHECK_SHAPE)convert_points_from_homogeneousconvert_points_to_homogeneous)transform_points) solve_cubic)_torch_svd_castsafe_inverse_with_mask:0yE>pointsepsreturnc Cst|jdkr t|j|jddkrt|jtj|ddd}||jdddjdd}ttd ||}t|t |}}t ||| |d ||| |d |||g dd}| ddd}t ||}||fS) 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@).rr).rr) lenshapeAssertionErrortorchmeannormsqrttensorr zeros_likerviewr)rrx_meanscaleonesr transform points_normr.X/home/ubuntu/.local/lib/python3.10/site-packages/kornia/geometry/epipolar/fundamental.pynormalize_points s  * r0McCsJt|jdkr t|j|dddddf}t||k||||S)aNormalize a given transformation matrix. The function trakes the transformation matrix and normalize so that the value in the last row and column is one. Args: M: The transformation to be normalized of any shape with a minimum size of 2x2. eps: small value to avoid unstabilities during the backpropagation. Returns: the normalized transformation matrix with same shape as the input. r.rN)rr r!r abs)r1rnorm_valr.r.r/normalize_transformationIs r4points1points2c Cs:t|gdt|gd|jd}t|\}}t|\}}tj|ddd\}}tj|ddd\} } t|} t| || || | || || ||| g d} t| \} } }|dddd}|dddd}t |d f|j |j d }tj |}tj |}||d d df<td |t|d||d d d f<td |t|d||d d df<||d d df<t|}t |dddf|j |j d }tj|d ddktj|d dd kB}|}t|}||ddfjd d||||ddfjd d}t|tjd|j |j d }d||||<||||||<|d |ddd}|d |ddd}||||d d d d f||||d d d d f||<t ddtjd}d|d<d|||f<d|||f<||d d|jddd}||d d|jddd}t|ddt|||||<t|S)ayCompute the fundamental matrix using the 7-point algorithm. Args: points1: A set of points in the first image with a tensor shape :math:`(B, N, 2)`. points2: A set of points in the second image with a tensor shape :math:`(B, N, 2)`. Returns: the computed fundamental matrix with shape :math:`(B, 3*m, 3), Valid values of m are 1, 2 or 3` )B72rrrrchunks).r).devicedtypeNzbii->brr?)rAT)rr)r r r0r"chunkrrrr(r r@rAlinalgdeteinsumrr count_nonzero unsqueezeiscloser&expandboolmatmul transposer4) r5r6 batch_size points1_norm transform1 points2_norm transform2x1y1x2y2r+X_vf1f2coeffsf1_detf2_detrootsfmatrixvalid_root_mask_lambda_mu_s_s_non_zero_mask f1_expanded f2_expandedmat_ind trans1_exp trans2_expr.r.r/ run_7point_s\    ,  (($ *   rmweightsc Cst|gdt|gdt|||jddkrt|j|dur9t|ddg|jd|jdks9t|jt|\}}t|\}}tj|ddd \}}tj|ddd \} } t|} tj| || || | || || ||| g dd } |dur| d d| } nt |} | d d| | } t | \}}}|d  dd d }t |\}}}tj gd|j|jd}|t ||| d d}| d d||}t|S)a3Compute the fundamental matrix using the DLT formulation. The linear system is solved by using the Weighted Least Squares Solution for the 8 Points algorithm. 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)`. Returns: the computed fundamental matrix with shape :math:`(B, 3, 3)`. )r7Nr9rr=Nr7rorrr:rrD).rr)rCrCrBr?)r r r r!r0r"rErcatrO diag_embedrr(r&r@rAr4)r5r6rnrQrRrSrTrUrVrWrXr+rYw_diagrZVF_matUS rank_mask F_projectedF_estr.r.r/ run_8points4     0 rz8POINTmethod)r{7POINTcCsF|dkr t||}|S|dkrt|||}|Std|d)aFind 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. r}r{zInvalid method: z.. Supported methods are '7POINT' and '8POINT'.)upperrmrz ValueError)r5r6rnr|resultr.r.r/find_fundamentals   rrtcCst|gd|jddkrt|}n|jddkr|}nt|jt|gdtj|ddd}tj||ddd\}}}||||}t|d kd t|t |}tj ||||||gdd }tj|dddS) a4Compute 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)`. )*roDIMrrrr3rrD)dim0dim1r:rBrCr) r r rr!r"rOrEr r%rrp)rrtpoints_habcnuliner.r.r/compute_correspond_epiliness     rlinescCst|gdt|gd|jddkrt|}n|jddkr$|}nt|j|tjgd|j|jdddd}tj j ||dd}|S) 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)`. )rror)rrotworr)rrr)rAr@rr) r r rr!r"r&rAr@r(rFcross)rrrinfinity_pointperpr.r.r/get_perpendicular4s   &rpts1pts2FmcCst|tstdt|t|jdks|jdddks&td|j|jddkr1t|}|jddkr.vstack.rrrrrr) r r r!rrAr"float32float64torprGreshaper()rrr input_dtypeX1X2X3Y1Y2Y3X1Y1X2Y1X3Y1X1Y2X2Y2X3Y2X1Y3X2Y3X3Y3F_vecr.r.r/fundamental_from_projectionss@   ..""" 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