Df<(dZddlZddlmZmZddlmZddlZ dZ dZ d*dZ d+dZ d Zd Zd ej fd Zd ej fdZdej dej dej dej fdZdej dej dej fdZdej dej dej fdZdej dej dej fdZdej dej dej fdZdej dej dej dej fdZdej dej dej dej fdZ d,ded efd!Zdej dej dej fd"Zd#ej dej fd$Zd%ej dej fd&Zd'ej dej fd(Zd)Z y)-z'Multi-view geometry & proejction code..N) rearrangerepeat) functionalc|dddf|dddf}}tj|d}|||zjdd|zz }tj|d}tj||d}tj |||fdS)N.dimTkeepdim)F normalizesumtorchcrossstack)d6a1a2b1b2b3s 6/home/cameronsmith/repos/minimal-diffusion/geometry.py d6_to_rotmatrs RaR["S!"W+B RR B rBwmmBm-2 2B RR B R $B ;;B| ,,ctdt||dz zdz t||dz z}}tg|dd||gfjd|}||k(r |dddf}t |d|}|S)Nrzb x y -> b trgt x y)trgt) maxint camera_interpunbindrrcat ones_likeeinsum)pose_inptime_in_trgteye_ptsij pose_interp query_ptss rtime_interp_posesr/s aFF1H%&q( )#ffQh.?*@aAD!QqE'!2!9!9!!<DVDK!t!A#[%:GK rc,t|}t||}t||jd\}} |dz dz} t | d} | dddf} t j || d||} | jd} t | d } | |ddd f|fS) Nr?zb n ch -> b n () ch.T) align_corners padding_modemoderzb ch n -> b n chr)homogenize_pointstransform_world2camproject unsqueezerr grid_samplesqueeze) coords_3d_world cam2world intrinsics img_featuresinterpr4 c3d_world_hom c3d_cam_homc2d_camdepthc2d_normfeatss rpixel_aligned_featuresrGs&o6M%mY?K[**>*>q*ABNGU# "H#89HRaR H MMhdTZ E MM" E e/ 0E +c2A2g& //rcPt|jdk(rht|jdd|jdd||jddnd}|d|dj d|jddfS t j dt j5|jddd}|jddd}||jddd}d}|t j|ddddf}||jdd d zz }||zjdd }||zjdd }||z }||z } t j|D cgc]&} t j| jd(c} } || zj| jddd} t j| \} }}t j | jd|j" j%d}|j'| jddd}|ddddfxxt j(t j*| j|jdddzcc<|j|j| jddd}||j|z }|j||z}t j ddj-|j/dddj1|}||dddd dd f<t j ddj-|j/dddj1|}|jd|dddd df<t j ddj-|j/dddj1|}||z|z}||z j3j5|fcdddScc} w#1swYyxYw) Nrrr2cuda) device_typedtypeTrr gư>devicer)lenshape procrustesflatten unflattenrautocastfloat32permuter%rrdiagr;bmmsvdeyerNr9rsigndetexpandsizetosquaremean)S1S2weightsout transposed weights_normmu1mu2X1X2wdiagsKUsVZRtS1_hatR_T_S_transfs rrQrQ4s 288}aAaAaQXQd19Mjno1vc!f&&q"1666 F%-- @02 ZZ!A  ZZ!A   OOAa*G ?oob2A2h/G Bt b k j)rarsqrtpowrr&rr)ctx_xyztrgt_xyzx_pointsy_pointsx_meany_meanx_points_centeredy_points_centeredx_scalex_points_normalizedy_scaley_points_normalizedMrsx_points_transformedlosss r rigidity_lossr|s)HH ]]1d] +F ]]1d] +F 6) 6)jj*..q155a5FGLLQX\L]G+g5jj*..q155a5FGLLQX\L]G+g5 ,.ACVWA#A&A!<<(;Q? #6 6 ; ;A > C C ED Krpointsctj|dddf|j}tj||fdS)zAppends a "1" to the coordinates of a (batch of) points of dimension DIM. Args: points: points of shape (..., DIM) Returns: points_hom: points with appended "1" dimension. .NrrMrr )rr%rNr$)roness rr6r6s9 ??6#rr'?6== AD 99fd^ ,,rvectorsctj|dddf|j}tj||fdS)zAppends a "0" to the coordinates of a (batch of) vectors of dimension DIM. Args: vectors: vectors of shape (..., DIM) Returns: vectors_hom: points with appended "0" dimension. .NrrMrr )r zeros_likerNr$)rzeross rhomogenize_vecsrs=   WS"1"W-gnn EE 99gu%2 ..rxy_pixzr>returncpt|}tjd|j|}||z}|S)awUnproject (lift) 2D pixel coordinates x_pix and per-pixel z coordinate to 3D points in camera coordinates. Args: xy_pix: 2D pixel coordinates of shape (..., 2) z: per-pixel depth, defined as z coordinate of shape (..., 1) intrinscis: camera intrinscics of shape (..., 3, 3) Returns: xyz_cam: points in 3D camera coordinates. ...ij,...kj->...ki)r6rr&inverse)rrr> xy_pix_homxyz_cams r unprojectrs8#6*Jll/1C1C1EzRG qLG Nr xyz_world_homr=cDtj|}t||S)aTransforms points from 3D world coordinates to 3D camera coordinates. Args: xyz_world_hom: homogenized 3D points of shape (..., 4) cam2world: camera pose of shape (..., 4, 4) Returns: xyz_cam: points in camera coordinates. )rrtransform_rigid)rr= world2cams rr7r7s i(I =) 44r xyz_cam_homct||S)aTransforms points from 3D world coordinates to 3D camera coordinates. Args: xyz_cam_hom: homogenized 3D points of shape (..., 4) cam2world: camera pose of shape (..., 4, 4) Returns: xyz_world: points in camera coordinates. )r)rr=s rtransform_cam2worldrs ; 22rxyz_homTc0tjd||S)zApply a rigid-body transform to a (batch of) points / vectors. Args: xyz_hom: homogenized 3D points of shape (..., 4) T: rigid-body transform matrix of shape (..., 4, 4) Returns: xyz_trans: transformed points. r)rr&)rrs rrrs <<,a 99rc jt|tj|dddf|j|S)N.rrM)r>)rrr%rN)rr>s r#get_unnormalized_cam_ray_directionsrs5  sBQBw > rc>|Gtjddj|jdddj |}|ddddf}t ||}|}t |}t||}t|d|jd}||dddffS) NrIrr.rzb ch -> b num_rays chr)num_rays) rrZr]r^r_rrrrrP)rr>r=cam_origin_world ray_dirs_cam rd_cam_hom rd_world_homs rget_world_rays_rs IIaL&--fkk!nRCFFvN !bqb"-7vzJLL!.J'z9=L1Lr=rers rget_world_raysrs  6<<!fnnQq1*2D2DQq2Idmdy)J[J[\]^_J`@DE9<=A Afll2A./== 6*Y 77>s&B y_resolution x_resolutionc  tjtjdd||tjdd||\}}tj|j |j gdj ddd}|S)aFor an image with y_resolution and x_resolution, return a tensor of pixel coordinates normalized to lie in [0, 1], with the origin (0, 0) in the top left corner, the x-axis pointing right, the y-axis pointing down, and the bottom right corner being at (1, 1). Returns: xy_pix: a meshgrid of values from [0, 1] of shape (y_resolution, x_resolution, 2) rr)stepsrNrr r2)rmeshgridlinspacerr}rV)rrrNr+r,rs rget_opencv_pixel_coordinatesr'sq >> q!<? q!<? DAq [[!'')QWWY/R 8 @ @Aq IF Mrct|jt|jk(r|jd}tjd||dddf}|dddf}||dzz }|dddf|fS) a9Projects homogenized 3D points xyz_cam_hom in camera coordinates to pixel coordinates. Args: xyz_cam_hom: 3D points of shape (..., 4) intrinsics: camera intrinscics of shape (..., 3, 3) Returns: xy: homogeneous pixel coordinates of shape (..., 3) (final coordinate is 1) rz...ij,...j->...i.Nrrgh㈵>r2)rOrPr9rr&)rr>xywrs rr8r8>s :  c+"3"344AUAUVWAXj ,,):{377K LC CH A T C sBQBw<?rrcptj|}|dkD}tj||||<|S)z[ Returns torch.sqrt(torch.max(0, x)) but with a zero subgradient where x is 0. r)rrr)rret positive_masks r_sqrt_positive_partrOs:   1 CEMAm$45C  Jrmatrixc <|jddk7s|jddk7rtd|jd|jdd}tj|j |dzd\ }}}}}}}} } t tjd |z|z| zd |z|z | z d |z |z| z d |z |z | zgd} tjtj| d d z| |z ||z ||z gdtj| |z | d d z||z||zgdtj||z ||z| d d z|| zgdtj||z ||z| |z| dd zgdgd} tjdj| j| j} | d| dj| zz }|tj| jdddkDddfj |dzS)z Convert rotations given as rotation matrices to quaternions. Args: matrix: Rotation matrices as tensor of shape (..., 3, 3). Returns: quaternions with real part first, as tensor of shape (..., 4). rrr zInvalid rotation matrix shape .N) r g?).rr2).r).r2).rg?)rLrN@).NrI) num_classesr1)rI)r^ ValueErrorrPrr#reshaperrtensorr_rLrNr rone_hotargmax)r batch_dimm00m01m02m10m11m12m20m21m22q_abs quat_by_rijkflrquat_candidatess rmatrix_to_quaternionrYs8{{2!v{{2!39&,,qIJJ Sb!I27,,y4'(b3/Cc3S#sC  c C#%c C#%c C#%c C#%     E;; KKv!+S3Yc 39MSU V KKsE&MQ$6c 39MSU V KKsC#IuV}/A39MSU V KKsC#IsSy%-1:LMSU V  L ,,s   U[[  FC"cE),<,@,@,E&EFO  %,,2,&A6r s9- $$-Zb06;2z  6 -ell - /U\\ / LL"\\7<|| \\( 5<< 5,1LL 5 \\ 5 3 3*/,, 3 \\ 3 :U\\ :ell :u|| : LL&+ll \\3 LL3 3||3 \\ 3>8 LL8 8||8 \\ 8 .5<<ELL" 5<< ELL 2 2 %,,2 f6ell6u||68#r