# Copyright (C) 2024-present Naver Corporation. All rights reserved. # Licensed under CC BY-NC-SA 4.0 (non-commercial use only). # # -------------------------------------------------------- # MASt3R Sparse Global Alignement # -------------------------------------------------------- from tqdm import tqdm import roma import torch import torch.nn as nn import torch.nn.functional as F import numpy as np import os from collections import namedtuple from functools import lru_cache from scipy import sparse as sp import copy from mast3r.utils.misc import mkdir_for, hash_md5 from mast3r.cloud_opt.utils.losses import gamma_loss from mast3r.cloud_opt.utils.schedules import linear_schedule, cosine_schedule from mast3r.fast_nn import fast_reciprocal_NNs, merge_corres import mast3r.utils.path_to_dust3r # noqa from dust3r.utils.geometry import inv, geotrf # noqa from dust3r.utils.device import to_cpu, to_numpy, todevice # noqa from dust3r.post_process import estimate_focal_knowing_depth # noqa from dust3r.optim_factory import adjust_learning_rate_by_lr # noqa from dust3r.viz import SceneViz class SparseGA(): def __init__(self, img_paths, pairs_in, res_fine, anchors, canonical_paths=None): def fetch_img(im): def torgb(x): return (x[0].permute(1, 2, 0).numpy() * .5 + .5).clip(min=0., max=1.) for im1, im2 in pairs_in: if im1['instance'] == im: return torgb(im1['img']) if im2['instance'] == im: return torgb(im2['img']) self.canonical_paths = canonical_paths self.img_paths = img_paths self.imgs = [fetch_img(img) for img in img_paths] self.intrinsics = res_fine['intrinsics'] self.cam2w = res_fine['cam2w'] self.depthmaps = res_fine['depthmaps'] self.pts3d = res_fine['pts3d'] self.pts3d_colors = [] self.working_device = self.cam2w.device for i in range(len(self.imgs)): im = self.imgs[i] x, y = anchors[i][0][..., :2].detach().cpu().numpy().T self.pts3d_colors.append(im[y, x]) assert self.pts3d_colors[-1].shape == self.pts3d[i].shape self.n_imgs = len(self.imgs) def get_focals(self): return torch.tensor([ff[0, 0] for ff in self.intrinsics]).to(self.working_device) def get_principal_points(self): return torch.stack([ff[:2, -1] for ff in self.intrinsics]).to(self.working_device) def get_im_poses(self): return self.cam2w def get_sparse_pts3d(self): return self.pts3d def get_dense_pts3d(self, clean_depth=True, subsample=8): assert self.canonical_paths, 'cache_path is required for dense 3d points' device = self.cam2w.device confs = [] base_focals = [] anchors = {} for i, canon_path in enumerate(self.canonical_paths): (canon, canon2, conf), focal = torch.load(canon_path, map_location=device) confs.append(conf) base_focals.append(focal) H, W = conf.shape pixels = torch.from_numpy(np.mgrid[:W, :H].T.reshape(-1, 2)).float().to(device) idxs, offsets = anchor_depth_offsets(canon2, {i: (pixels, None)}, subsample=subsample) anchors[i] = (pixels, idxs[i], offsets[i]) # densify sparse depthmaps pts3d, depthmaps = make_pts3d(anchors, self.intrinsics, self.cam2w, [ d.ravel() for d in self.depthmaps], base_focals=base_focals, ret_depth=True) return pts3d, depthmaps, confs def get_pts3d_colors(self): return self.pts3d_colors def get_depthmaps(self): return self.depthmaps def get_masks(self): return [slice(None, None) for _ in range(len(self.imgs))] def show(self, show_cams=True): pts3d, _, confs = self.get_dense_pts3d() show_reconstruction(self.imgs, self.intrinsics if show_cams else None, self.cam2w, [p.clip(min=-50, max=50) for p in pts3d], masks=[c > 1 for c in confs]) def convert_dust3r_pairs_naming(imgs, pairs_in): for pair_id in range(len(pairs_in)): for i in range(2): pairs_in[pair_id][i]['instance'] = imgs[pairs_in[pair_id][i]['idx']] return pairs_in def sparse_global_alignment(imgs, pairs_in, cache_path, model, subsample=8, desc_conf='desc_conf', device='cuda', dtype=torch.float32, shared_intrinsics=False, **kw): """ Sparse alignment with MASt3R imgs: list of image paths cache_path: path where to dump temporary files (str) lr1, niter1: learning rate and #iterations for coarse global alignment (3D matching) lr2, niter2: learning rate and #iterations for refinement (2D reproj error) lora_depth: smart dimensionality reduction with depthmaps """ # Convert pair naming convention from dust3r to mast3r pairs_in = convert_dust3r_pairs_naming(imgs, pairs_in) # forward pass pairs, cache_path = forward_mast3r(pairs_in, model, cache_path=cache_path, subsample=subsample, desc_conf=desc_conf, device=device) # extract canonical pointmaps tmp_pairs, pairwise_scores, canonical_views, canonical_paths, preds_21 = \ prepare_canonical_data(imgs, pairs, subsample, cache_path=cache_path, mode='avg-angle', device=device) # compute minimal spanning tree mst = compute_min_spanning_tree(pairwise_scores) # remove all edges not in the spanning tree? # min_spanning_tree = {(imgs[i],imgs[j]) for i,j in mst[1]} # tmp_pairs = {(a,b):v for (a,b),v in tmp_pairs.items() if {(a,b),(b,a)} & min_spanning_tree} # smartly combine all useful data imsizes, pps, base_focals, core_depth, anchors, corres, corres2d, preds_21 = \ condense_data(imgs, tmp_pairs, canonical_views, preds_21, dtype) imgs, res_coarse, res_fine = sparse_scene_optimizer( imgs, subsample, imsizes, pps, base_focals, core_depth, anchors, corres, corres2d, preds_21, canonical_paths, mst, shared_intrinsics=shared_intrinsics, cache_path=cache_path, device=device, dtype=dtype, **kw) return SparseGA(imgs, pairs_in, res_fine or res_coarse, anchors, canonical_paths) def sparse_scene_optimizer(imgs, subsample, imsizes, pps, base_focals, core_depth, anchors, corres, corres2d, preds_21, canonical_paths, mst, cache_path, lr1=0.2, niter1=500, loss1=gamma_loss(1.1), lr2=0.02, niter2=500, loss2=gamma_loss(0.4), lossd=gamma_loss(1.1), opt_pp=True, opt_depth=True, schedule=cosine_schedule, depth_mode='add', exp_depth=False, lora_depth=False, # dict(k=96, gamma=15, min_norm=.5), shared_intrinsics=False, init={}, device='cuda', dtype=torch.float32, matching_conf_thr=5., loss_dust3r_w=0.01, verbose=True, dbg=()): init = copy.deepcopy(init) # extrinsic parameters vec0001 = torch.tensor((0, 0, 0, 1), dtype=dtype, device=device) quats = [nn.Parameter(vec0001.clone()) for _ in range(len(imgs))] trans = [nn.Parameter(torch.zeros(3, device=device, dtype=dtype)) for _ in range(len(imgs))] # initialize ones = torch.ones((len(imgs), 1), device=device, dtype=dtype) median_depths = torch.ones(len(imgs), device=device, dtype=dtype) for img in imgs: idx = imgs.index(img) init_values = init.setdefault(img, {}) if verbose and init_values: print(f' >> initializing img=...{img[-25:]} [{idx}] for {set(init_values)}') K = init_values.get('intrinsics') if K is not None: K = K.detach() focal = K[:2, :2].diag().mean() pp = K[:2, 2] base_focals[idx] = focal pps[idx] = pp pps[idx] /= imsizes[idx] # default principal_point would be (0.5, 0.5) depth = init_values.get('depthmap') if depth is not None: core_depth[idx] = depth.detach() median_depths[idx] = med_depth = core_depth[idx].median() core_depth[idx] /= med_depth cam2w = init_values.get('cam2w') if cam2w is not None: rot = cam2w[:3, :3].detach() cam_center = cam2w[:3, 3].detach() quats[idx].data[:] = roma.rotmat_to_unitquat(rot) trans_offset = med_depth * torch.cat((imsizes[idx] / base_focals[idx] * (0.5 - pps[idx]), ones[:1, 0])) trans[idx].data[:] = cam_center + rot @ trans_offset del rot assert False, 'inverse kinematic chain not yet implemented' # intrinsics parameters if shared_intrinsics: # Optimize a single set of intrinsics for all cameras. Use averages as init. confs = torch.stack([torch.load(pth)[0][2].mean() for pth in canonical_paths]).to(pps) weighting = confs / confs.sum() pp = nn.Parameter((weighting @ pps).to(dtype)) pps = [pp for _ in range(len(imgs))] focal_m = weighting @ base_focals log_focal = nn.Parameter(focal_m.view(1).log().to(dtype)) log_focals = [log_focal for _ in range(len(imgs))] else: pps = [nn.Parameter(pp.to(dtype)) for pp in pps] log_focals = [nn.Parameter(f.view(1).log().to(dtype)) for f in base_focals] diags = imsizes.float().norm(dim=1) min_focals = 0.25 * diags # diag = 1.2~1.4*max(W,H) => beta >= 1/(2*1.2*tan(fov/2)) ~= 0.26 max_focals = 10 * diags assert len(mst[1]) == len(pps) - 1 def make_K_cam_depth(log_focals, pps, trans, quats, log_sizes, core_depth): # make intrinsics focals = torch.cat(log_focals).exp().clip(min=min_focals, max=max_focals) pps = torch.stack(pps) K = torch.eye(3, dtype=dtype, device=device)[None].expand(len(imgs), 3, 3).clone() K[:, 0, 0] = K[:, 1, 1] = focals K[:, 0:2, 2] = pps * imsizes if trans is None: return K # security! optimization is always trying to crush the scale down sizes = torch.cat(log_sizes).exp() global_scaling = 1 / sizes.min() # compute distance of camera to focal plane # tan(fov) = W/2 / focal z_cameras = sizes * median_depths * focals / base_focals # make extrinsic rel_cam2cam = torch.eye(4, dtype=dtype, device=device)[None].expand(len(imgs), 4, 4).clone() rel_cam2cam[:, :3, :3] = roma.unitquat_to_rotmat(F.normalize(torch.stack(quats), dim=1)) rel_cam2cam[:, :3, 3] = torch.stack(trans) # camera are defined as a kinematic chain tmp_cam2w = [None] * len(K) tmp_cam2w[mst[0]] = rel_cam2cam[mst[0]] for i, j in mst[1]: # i is the cam_i_to_world reference, j is the relative pose = cam_j_to_cam_i tmp_cam2w[j] = tmp_cam2w[i] @ rel_cam2cam[j] tmp_cam2w = torch.stack(tmp_cam2w) # smart reparameterizaton of cameras trans_offset = z_cameras.unsqueeze(1) * torch.cat((imsizes / focals.unsqueeze(1) * (0.5 - pps), ones), dim=-1) new_trans = global_scaling * (tmp_cam2w[:, :3, 3:4] - tmp_cam2w[:, :3, :3] @ trans_offset.unsqueeze(-1)) cam2w = torch.cat((torch.cat((tmp_cam2w[:, :3, :3], new_trans), dim=2), vec0001.view(1, 1, 4).expand(len(K), 1, 4)), dim=1) depthmaps = [] for i in range(len(imgs)): core_depth_img = core_depth[i] if exp_depth: core_depth_img = core_depth_img.exp() if lora_depth: # compute core_depth as a low-rank decomposition of 3d points core_depth_img = lora_depth_proj[i] @ core_depth_img if depth_mode == 'add': core_depth_img = z_cameras[i] + (core_depth_img - 1) * (median_depths[i] * sizes[i]) elif depth_mode == 'mul': core_depth_img = z_cameras[i] * core_depth_img else: raise ValueError(f'Bad {depth_mode=}') depthmaps.append(global_scaling * core_depth_img) return K, (inv(cam2w), cam2w), depthmaps K = make_K_cam_depth(log_focals, pps, None, None, None, None) if shared_intrinsics: print('init focal (shared) = ', to_numpy(K[0, 0, 0]).round(2)) else: print('init focals =', to_numpy(K[:, 0, 0])) # spectral low-rank projection of depthmaps if lora_depth: core_depth, lora_depth_proj = spectral_projection_of_depthmaps( imgs, K, core_depth, subsample, cache_path=cache_path, **lora_depth) if exp_depth: core_depth = [d.clip(min=1e-4).log() for d in core_depth] core_depth = [nn.Parameter(d.ravel().to(dtype)) for d in core_depth] log_sizes = [nn.Parameter(torch.zeros(1, dtype=dtype, device=device)) for _ in range(len(imgs))] # Fetch img slices _, confs_sum, imgs_slices = corres # Define which pairs are fine to use with matching def matching_check(x): return x.max() > matching_conf_thr is_matching_ok = {} for s in imgs_slices: is_matching_ok[s.img1, s.img2] = matching_check(s.confs) # Prepare slices and corres for losses dust3r_slices = [s for s in imgs_slices if not is_matching_ok[s.img1, s.img2]] loss3d_slices = [s for s in imgs_slices if is_matching_ok[s.img1, s.img2]] cleaned_corres2d = [] for cci, (img1, pix1, confs, confsum, imgs_slices) in enumerate(corres2d): cf_sum = 0 pix1_filtered = [] confs_filtered = [] curstep = 0 cleaned_slices = [] for img2, slice2 in imgs_slices: if is_matching_ok[img1, img2]: tslice = slice(curstep, curstep + slice2.stop - slice2.start, slice2.step) pix1_filtered.append(pix1[tslice]) confs_filtered.append(confs[tslice]) cleaned_slices.append((img2, slice2)) curstep += slice2.stop - slice2.start if pix1_filtered != []: pix1_filtered = torch.cat(pix1_filtered) confs_filtered = torch.cat(confs_filtered) cf_sum = confs_filtered.sum() cleaned_corres2d.append((img1, pix1_filtered, confs_filtered, cf_sum, cleaned_slices)) def loss_dust3r(cam2w, pts3d, pix_loss): # In the case no correspondence could be established, fallback to DUSt3R GA regression loss formulation (sparsified) loss = 0. cf_sum = 0. for s in dust3r_slices: if init[imgs[s.img1]].get('freeze') and init[imgs[s.img2]].get('freeze'): continue # fallback to dust3r regression tgt_pts, tgt_confs = preds_21[imgs[s.img2]][imgs[s.img1]] tgt_pts = geotrf(cam2w[s.img2], tgt_pts) cf_sum += tgt_confs.sum() loss += tgt_confs @ pix_loss(pts3d[s.img1], tgt_pts) return loss / cf_sum if cf_sum != 0. else 0. def loss_3d(K, w2cam, pts3d, pix_loss): # For each correspondence, we have two 3D points (one for each image of the pair). # For each 3D point, we have 2 reproj errors if any(v.get('freeze') for v in init.values()): pts3d_1 = [] pts3d_2 = [] confs = [] for s in loss3d_slices: if init[imgs[s.img1]].get('freeze') and init[imgs[s.img2]].get('freeze'): continue pts3d_1.append(pts3d[s.img1][s.slice1]) pts3d_2.append(pts3d[s.img2][s.slice2]) confs.append(s.confs) else: pts3d_1 = [pts3d[s.img1][s.slice1] for s in loss3d_slices] pts3d_2 = [pts3d[s.img2][s.slice2] for s in loss3d_slices] confs = [s.confs for s in loss3d_slices] if pts3d_1 != []: confs = torch.cat(confs) pts3d_1 = torch.cat(pts3d_1) pts3d_2 = torch.cat(pts3d_2) loss = confs @ pix_loss(pts3d_1, pts3d_2) cf_sum = confs.sum() else: loss = 0. cf_sum = 1. return loss / cf_sum def loss_2d(K, w2cam, pts3d, pix_loss): # For each correspondence, we have two 3D points (one for each image of the pair). # For each 3D point, we have 2 reproj errors proj_matrix = K @ w2cam[:, :3] loss = npix = 0 for img1, pix1_filtered, confs_filtered, cf_sum, cleaned_slices in cleaned_corres2d: if init[imgs[img1]].get('freeze', 0) >= 1: continue # no need pts3d_in_img1 = [pts3d[img2][slice2] for img2, slice2 in cleaned_slices] if pts3d_in_img1 != []: pts3d_in_img1 = torch.cat(pts3d_in_img1) loss += confs_filtered @ pix_loss(pix1_filtered, reproj2d(proj_matrix[img1], pts3d_in_img1)) npix += confs_filtered.sum() return loss / npix if npix != 0 else 0. def optimize_loop(loss_func, lr_base, niter, pix_loss, lr_end=0): # create optimizer params = pps + log_focals + quats + trans + log_sizes + core_depth optimizer = torch.optim.Adam(params, lr=1, weight_decay=0, betas=(0.9, 0.9)) ploss = pix_loss if 'meta' in repr(pix_loss) else (lambda a: pix_loss) with tqdm(total=niter) as bar: for iter in range(niter or 1): K, (w2cam, cam2w), depthmaps = make_K_cam_depth(log_focals, pps, trans, quats, log_sizes, core_depth) pts3d = make_pts3d(anchors, K, cam2w, depthmaps, base_focals=base_focals) if niter == 0: break alpha = (iter / niter) lr = schedule(alpha, lr_base, lr_end) adjust_learning_rate_by_lr(optimizer, lr) pix_loss = ploss(1 - alpha) optimizer.zero_grad() loss = loss_func(K, w2cam, pts3d, pix_loss) + loss_dust3r_w * loss_dust3r(cam2w, pts3d, lossd) loss.backward() optimizer.step() # make sure the pose remains well optimizable for i in range(len(imgs)): quats[i].data[:] /= quats[i].data.norm() loss = float(loss) if loss != loss: break # NaN loss bar.set_postfix_str(f'{lr=:.4f}, {loss=:.3f}') bar.update(1) if niter: print(f'>> final loss = {loss}') return dict(intrinsics=K.detach(), cam2w=cam2w.detach(), depthmaps=[d.detach() for d in depthmaps], pts3d=[p.detach() for p in pts3d]) # at start, don't optimize 3d points for i, img in enumerate(imgs): trainable = not (init[img].get('freeze')) pps[i].requires_grad_(False) log_focals[i].requires_grad_(False) quats[i].requires_grad_(trainable) trans[i].requires_grad_(trainable) log_sizes[i].requires_grad_(trainable) core_depth[i].requires_grad_(False) res_coarse = optimize_loop(loss_3d, lr_base=lr1, niter=niter1, pix_loss=loss1) res_fine = None if niter2: # now we can optimize 3d points for i, img in enumerate(imgs): if init[img].get('freeze', 0) >= 1: continue pps[i].requires_grad_(bool(opt_pp)) log_focals[i].requires_grad_(True) core_depth[i].requires_grad_(opt_depth) # refinement with 2d reproj res_fine = optimize_loop(loss_2d, lr_base=lr2, niter=niter2, pix_loss=loss2) K = make_K_cam_depth(log_focals, pps, None, None, None, None) if shared_intrinsics: print('Final focal (shared) = ', to_numpy(K[0, 0, 0]).round(2)) else: print('Final focals =', to_numpy(K[:, 0, 0])) return imgs, res_coarse, res_fine @lru_cache def mask110(device, dtype): return torch.tensor((1, 1, 0), device=device, dtype=dtype) def proj3d(inv_K, pixels, z): if pixels.shape[-1] == 2: pixels = torch.cat((pixels, torch.ones_like(pixels[..., :1])), dim=-1) return z.unsqueeze(-1) * (pixels * inv_K.diag() + inv_K[:, 2] * mask110(z.device, z.dtype)) def make_pts3d(anchors, K, cam2w, depthmaps, base_focals=None, ret_depth=False): focals = K[:, 0, 0] invK = inv(K) all_pts3d = [] depth_out = [] for img, (pixels, idxs, offsets) in anchors.items(): # from depthmaps to 3d points if base_focals is None: pass else: # compensate for focal # depth + depth * (offset - 1) * base_focal / focal # = depth * (1 + (offset - 1) * (base_focal / focal)) offsets = 1 + (offsets - 1) * (base_focals[img] / focals[img]) pts3d = proj3d(invK[img], pixels, depthmaps[img][idxs] * offsets) if ret_depth: depth_out.append(pts3d[..., 2]) # before camera rotation # rotate to world coordinate pts3d = geotrf(cam2w[img], pts3d) all_pts3d.append(pts3d) if ret_depth: return all_pts3d, depth_out return all_pts3d def make_dense_pts3d(intrinsics, cam2w, depthmaps, canonical_paths, subsample, device='cuda'): base_focals = [] anchors = {} confs = [] for i, canon_path in enumerate(canonical_paths): (canon, canon2, conf), focal = torch.load(canon_path, map_location=device) confs.append(conf) base_focals.append(focal) H, W = conf.shape pixels = torch.from_numpy(np.mgrid[:W, :H].T.reshape(-1, 2)).float().to(device) idxs, offsets = anchor_depth_offsets(canon2, {i: (pixels, None)}, subsample=subsample) anchors[i] = (pixels, idxs[i], offsets[i]) # densify sparse depthmaps pts3d, depthmaps_out = make_pts3d(anchors, intrinsics, cam2w, [ d.ravel() for d in depthmaps], base_focals=base_focals, ret_depth=True) return pts3d, depthmaps_out, confs @torch.no_grad() def forward_mast3r(pairs, model, cache_path, desc_conf='desc_conf', device='cuda', subsample=8, **matching_kw): res_paths = {} for img1, img2 in tqdm(pairs): idx1 = hash_md5(img1['instance']) idx2 = hash_md5(img2['instance']) path1 = cache_path + f'/forward/{idx1}/{idx2}.pth' path2 = cache_path + f'/forward/{idx2}/{idx1}.pth' path_corres = cache_path + f'/corres_conf={desc_conf}_{subsample=}/{idx1}-{idx2}.pth' path_corres2 = cache_path + f'/corres_conf={desc_conf}_{subsample=}/{idx2}-{idx1}.pth' if os.path.isfile(path_corres2) and not os.path.isfile(path_corres): score, (xy1, xy2, confs) = torch.load(path_corres2) torch.save((score, (xy2, xy1, confs)), path_corres) if not all(os.path.isfile(p) for p in (path1, path2, path_corres)): if model is None: continue res = symmetric_inference(model, img1, img2, device=device) X11, X21, X22, X12 = [r['pts3d'][0] for r in res] C11, C21, C22, C12 = [r['conf'][0] for r in res] descs = [r['desc'][0] for r in res] qonfs = [r[desc_conf][0] for r in res] # save torch.save(to_cpu((X11, C11, X21, C21)), mkdir_for(path1)) torch.save(to_cpu((X22, C22, X12, C12)), mkdir_for(path2)) # perform reciprocal matching corres = extract_correspondences(descs, qonfs, device=device, subsample=subsample) conf_score = (C11.mean() * C12.mean() * C21.mean() * C22.mean()).sqrt().sqrt() matching_score = (float(conf_score), float(corres[2].sum()), len(corres[2])) if cache_path is not None: torch.save((matching_score, corres), mkdir_for(path_corres)) res_paths[img1['instance'], img2['instance']] = (path1, path2), path_corres del model torch.cuda.empty_cache() return res_paths, cache_path def symmetric_inference(model, img1, img2, device): shape1 = torch.from_numpy(img1['true_shape']).to(device, non_blocking=True) shape2 = torch.from_numpy(img2['true_shape']).to(device, non_blocking=True) img1 = img1['img'].to(device, non_blocking=True) img2 = img2['img'].to(device, non_blocking=True) # compute encoder only once feat1, feat2, pos1, pos2 = model._encode_image_pairs(img1, img2, shape1, shape2) def decoder(feat1, feat2, pos1, pos2, shape1, shape2): dec1, dec2 = model._decoder(feat1, pos1, feat2, pos2) with torch.cuda.amp.autocast(enabled=False): res1 = model._downstream_head(1, [tok.float() for tok in dec1], shape1) res2 = model._downstream_head(2, [tok.float() for tok in dec2], shape2) return res1, res2 # decoder 1-2 res11, res21 = decoder(feat1, feat2, pos1, pos2, shape1, shape2) # decoder 2-1 res22, res12 = decoder(feat2, feat1, pos2, pos1, shape2, shape1) return (res11, res21, res22, res12) def extract_correspondences(feats, qonfs, subsample=8, device=None, ptmap_key='pred_desc'): feat11, feat21, feat22, feat12 = feats qonf11, qonf21, qonf22, qonf12 = qonfs assert feat11.shape[:2] == feat12.shape[:2] == qonf11.shape == qonf12.shape assert feat21.shape[:2] == feat22.shape[:2] == qonf21.shape == qonf22.shape if '3d' in ptmap_key: opt = dict(device='cpu', workers=32) else: opt = dict(device=device, dist='dot', block_size=2**13) # matching the two pairs idx1 = [] idx2 = [] qonf1 = [] qonf2 = [] # TODO add non symmetric / pixel_tol options for A, B, QA, QB in [(feat11, feat21, qonf11.cpu(), qonf21.cpu()), (feat12, feat22, qonf12.cpu(), qonf22.cpu())]: nn1to2 = fast_reciprocal_NNs(A, B, subsample_or_initxy1=subsample, ret_xy=False, **opt) nn2to1 = fast_reciprocal_NNs(B, A, subsample_or_initxy1=subsample, ret_xy=False, **opt) idx1.append(np.r_[nn1to2[0], nn2to1[1]]) idx2.append(np.r_[nn1to2[1], nn2to1[0]]) qonf1.append(QA.ravel()[idx1[-1]]) qonf2.append(QB.ravel()[idx2[-1]]) # merge corres from opposite pairs H1, W1 = feat11.shape[:2] H2, W2 = feat22.shape[:2] cat = np.concatenate xy1, xy2, idx = merge_corres(cat(idx1), cat(idx2), (H1, W1), (H2, W2), ret_xy=True, ret_index=True) corres = (xy1.copy(), xy2.copy(), np.sqrt(cat(qonf1)[idx] * cat(qonf2)[idx])) return todevice(corres, device) @torch.no_grad() def prepare_canonical_data(imgs, tmp_pairs, subsample, order_imgs=False, min_conf_thr=0, cache_path=None, device='cuda', **kw): canonical_views = {} pairwise_scores = torch.zeros((len(imgs), len(imgs)), device=device) canonical_paths = [] preds_21 = {} for img in tqdm(imgs): if cache_path: cache = os.path.join(cache_path, 'canon_views', hash_md5(img) + f'_{subsample=}_{kw=}.pth') canonical_paths.append(cache) try: (canon, canon2, cconf), focal = torch.load(cache, map_location=device) except IOError: # cache does not exist yet, we create it! canon = focal = None # collect all pred1 n_pairs = sum((img in pair) for pair in tmp_pairs) ptmaps11 = None pixels = {} n = 0 for (img1, img2), ((path1, path2), path_corres) in tmp_pairs.items(): score = None if img == img1: X, C, X2, C2 = torch.load(path1, map_location=device) score, (xy1, xy2, confs) = load_corres(path_corres, device, min_conf_thr) pixels[img2] = xy1, confs if img not in preds_21: preds_21[img] = {} # Subsample preds_21 preds_21[img][img2] = X2[::subsample, ::subsample].reshape(-1, 3), C2[::subsample, ::subsample].ravel() if img == img2: X, C, X2, C2 = torch.load(path2, map_location=device) score, (xy1, xy2, confs) = load_corres(path_corres, device, min_conf_thr) pixels[img1] = xy2, confs if img not in preds_21: preds_21[img] = {} preds_21[img][img1] = X2[::subsample, ::subsample].reshape(-1, 3), C2[::subsample, ::subsample].ravel() if score is not None: i, j = imgs.index(img1), imgs.index(img2) # score = score[0] # score = np.log1p(score[2]) score = score[2] pairwise_scores[i, j] = score pairwise_scores[j, i] = score if canon is not None: continue if ptmaps11 is None: H, W = C.shape ptmaps11 = torch.empty((n_pairs, H, W, 3), device=device) confs11 = torch.empty((n_pairs, H, W), device=device) ptmaps11[n] = X confs11[n] = C n += 1 if canon is None: canon, canon2, cconf = canonical_view(ptmaps11, confs11, subsample, **kw) del ptmaps11 del confs11 # compute focals H, W = canon.shape[:2] pp = torch.tensor([W / 2, H / 2], device=device) if focal is None: focal = estimate_focal_knowing_depth(canon[None], pp, focal_mode='weiszfeld', min_focal=0.5, max_focal=3.5) if cache: torch.save(to_cpu(((canon, canon2, cconf), focal)), mkdir_for(cache)) # extract depth offsets with correspondences core_depth = canon[subsample // 2::subsample, subsample // 2::subsample, 2] idxs, offsets = anchor_depth_offsets(canon2, pixels, subsample=subsample) canonical_views[img] = (pp, (H, W), focal.view(1), core_depth, pixels, idxs, offsets) return tmp_pairs, pairwise_scores, canonical_views, canonical_paths, preds_21 def load_corres(path_corres, device, min_conf_thr): score, (xy1, xy2, confs) = torch.load(path_corres, map_location=device) valid = confs > min_conf_thr if min_conf_thr else slice(None) # valid = (xy1 > 0).all(dim=1) & (xy2 > 0).all(dim=1) & (xy1 < 512).all(dim=1) & (xy2 < 512).all(dim=1) # print(f'keeping {valid.sum()} / {len(valid)} correspondences') return score, (xy1[valid], xy2[valid], confs[valid]) PairOfSlices = namedtuple( 'ImgPair', 'img1, slice1, pix1, anchor_idxs1, img2, slice2, pix2, anchor_idxs2, confs, confs_sum') def condense_data(imgs, tmp_paths, canonical_views, preds_21, dtype=torch.float32): # aggregate all data properly set_imgs = set(imgs) principal_points = [] shapes = [] focals = [] core_depth = [] img_anchors = {} tmp_pixels = {} for idx1, img1 in enumerate(imgs): # load stuff pp, shape, focal, anchors, pixels_confs, idxs, offsets = canonical_views[img1] principal_points.append(pp) shapes.append(shape) focals.append(focal) core_depth.append(anchors) img_uv1 = [] img_idxs = [] img_offs = [] cur_n = [0] for img2, (pixels, match_confs) in pixels_confs.items(): if img2 not in set_imgs: continue assert len(pixels) == len(idxs[img2]) == len(offsets[img2]) img_uv1.append(torch.cat((pixels, torch.ones_like(pixels[:, :1])), dim=-1)) img_idxs.append(idxs[img2]) img_offs.append(offsets[img2]) cur_n.append(cur_n[-1] + len(pixels)) # store the position of 3d points tmp_pixels[img1, img2] = pixels.to(dtype), match_confs.to(dtype), slice(*cur_n[-2:]) img_anchors[idx1] = (torch.cat(img_uv1), torch.cat(img_idxs), torch.cat(img_offs)) all_confs = [] imgs_slices = [] corres2d = {img: [] for img in range(len(imgs))} for img1, img2 in tmp_paths: try: pix1, confs1, slice1 = tmp_pixels[img1, img2] pix2, confs2, slice2 = tmp_pixels[img2, img1] except KeyError: continue img1 = imgs.index(img1) img2 = imgs.index(img2) confs = (confs1 * confs2).sqrt() # prepare for loss_3d all_confs.append(confs) anchor_idxs1 = canonical_views[imgs[img1]][5][imgs[img2]] anchor_idxs2 = canonical_views[imgs[img2]][5][imgs[img1]] imgs_slices.append(PairOfSlices(img1, slice1, pix1, anchor_idxs1, img2, slice2, pix2, anchor_idxs2, confs, float(confs.sum()))) # prepare for loss_2d corres2d[img1].append((pix1, confs, img2, slice2)) corres2d[img2].append((pix2, confs, img1, slice1)) all_confs = torch.cat(all_confs) corres = (all_confs, float(all_confs.sum()), imgs_slices) def aggreg_matches(img1, list_matches): pix1, confs, img2, slice2 = zip(*list_matches) all_pix1 = torch.cat(pix1).to(dtype) all_confs = torch.cat(confs).to(dtype) return img1, all_pix1, all_confs, float(all_confs.sum()), [(j, sl2) for j, sl2 in zip(img2, slice2)] corres2d = [aggreg_matches(img, m) for img, m in corres2d.items()] imsizes = torch.tensor([(W, H) for H, W in shapes], device=pp.device) # (W,H) principal_points = torch.stack(principal_points) focals = torch.cat(focals) # Subsample preds_21 subsamp_preds_21 = {} for imk, imv in preds_21.items(): subsamp_preds_21[imk] = {} for im2k, (pred, conf) in preds_21[imk].items(): idxs = img_anchors[imgs.index(im2k)][1] subsamp_preds_21[imk][im2k] = (pred[idxs], conf[idxs]) # anchors subsample return imsizes, principal_points, focals, core_depth, img_anchors, corres, corres2d, subsamp_preds_21 def canonical_view(ptmaps11, confs11, subsample, mode='avg-angle'): assert len(ptmaps11) == len(confs11) > 0, 'not a single view1 for img={i}' # canonical pointmap is just a weighted average confs11 = confs11.unsqueeze(-1) - 0.999 canon = (confs11 * ptmaps11).sum(0) / confs11.sum(0) canon_depth = ptmaps11[..., 2].unsqueeze(1) S = slice(subsample // 2, None, subsample) center_depth = canon_depth[:, :, S, S] center_depth = torch.clip(center_depth, min=torch.finfo(center_depth.dtype).eps) stacked_depth = F.pixel_unshuffle(canon_depth, subsample) stacked_confs = F.pixel_unshuffle(confs11[:, None, :, :, 0], subsample) if mode == 'avg-reldepth': rel_depth = stacked_depth / center_depth stacked_canon = (stacked_confs * rel_depth).sum(dim=0) / stacked_confs.sum(dim=0) canon2 = F.pixel_shuffle(stacked_canon.unsqueeze(0), subsample).squeeze() elif mode == 'avg-angle': xy = ptmaps11[..., 0:2].permute(0, 3, 1, 2) stacked_xy = F.pixel_unshuffle(xy, subsample) B, _, H, W = stacked_xy.shape stacked_radius = (stacked_xy.view(B, 2, -1, H, W) - xy[:, :, None, S, S]).norm(dim=1) stacked_radius.clip_(min=1e-8) stacked_angle = torch.arctan((stacked_depth - center_depth) / stacked_radius) avg_angle = (stacked_confs * stacked_angle).sum(dim=0) / stacked_confs.sum(dim=0) # back to depth stacked_depth = stacked_radius.mean(dim=0) * torch.tan(avg_angle) canon2 = F.pixel_shuffle((1 + stacked_depth / canon[S, S, 2]).unsqueeze(0), subsample).squeeze() else: raise ValueError(f'bad {mode=}') confs = (confs11.square().sum(dim=0) / confs11.sum(dim=0)).squeeze() return canon, canon2, confs def anchor_depth_offsets(canon_depth, pixels, subsample=8): device = canon_depth.device # create a 2D grid of anchor 3D points H1, W1 = canon_depth.shape yx = np.mgrid[subsample // 2:H1:subsample, subsample // 2:W1:subsample] H2, W2 = yx.shape[1:] cy, cx = yx.reshape(2, -1) core_depth = canon_depth[cy, cx] assert (core_depth > 0).all() # slave 3d points (attached to core 3d points) core_idxs = {} # core_idxs[img2] = {corr_idx:core_idx} core_offs = {} # core_offs[img2] = {corr_idx:3d_offset} for img2, (xy1, _confs) in pixels.items(): px, py = xy1.long().T # find nearest anchor == block quantization core_idx = (py // subsample) * W2 + (px // subsample) core_idxs[img2] = core_idx.to(device) # compute relative depth offsets w.r.t. anchors ref_z = core_depth[core_idx] pts_z = canon_depth[py, px] offset = pts_z / ref_z core_offs[img2] = offset.detach().to(device) return core_idxs, core_offs def spectral_clustering(graph, k=None, normalized_cuts=False): graph.fill_diagonal_(0) # graph laplacian degrees = graph.sum(dim=-1) laplacian = torch.diag(degrees) - graph if normalized_cuts: i_inv = torch.diag(degrees.sqrt().reciprocal()) laplacian = i_inv @ laplacian @ i_inv # compute eigenvectors! eigval, eigvec = torch.linalg.eigh(laplacian) return eigval[:k], eigvec[:, :k] def sim_func(p1, p2, gamma): diff = (p1 - p2).norm(dim=-1) avg_depth = (p1[:, :, 2] + p2[:, :, 2]) rel_distance = diff / avg_depth sim = torch.exp(-gamma * rel_distance.square()) return sim def backproj(K, depthmap, subsample): H, W = depthmap.shape uv = np.mgrid[subsample // 2:subsample * W:subsample, subsample // 2:subsample * H:subsample].T.reshape(H, W, 2) xyz = depthmap.unsqueeze(-1) * geotrf(inv(K), todevice(uv, K.device), ncol=3) return xyz def spectral_projection_depth(K, depthmap, subsample, k=64, cache_path='', normalized_cuts=True, gamma=7, min_norm=5): try: if cache_path: cache_path = cache_path + f'_{k=}_norm={normalized_cuts}_{gamma=}.pth' lora_proj = torch.load(cache_path, map_location=K.device) except IOError: # reconstruct 3d points in camera coordinates xyz = backproj(K, depthmap, subsample) # compute all distances xyz = xyz.reshape(-1, 3) graph = sim_func(xyz[:, None], xyz[None, :], gamma=gamma) _, lora_proj = spectral_clustering(graph, k, normalized_cuts=normalized_cuts) if cache_path: torch.save(lora_proj.cpu(), mkdir_for(cache_path)) lora_proj, coeffs = lora_encode_normed(lora_proj, depthmap.ravel(), min_norm=min_norm) # depthmap ~= lora_proj @ coeffs return coeffs, lora_proj def lora_encode_normed(lora_proj, x, min_norm, global_norm=False): # encode the pointmap coeffs = torch.linalg.pinv(lora_proj) @ x # rectify the norm of basis vector to be ~ equal if coeffs.ndim == 1: coeffs = coeffs[:, None] if global_norm: lora_proj *= coeffs[1:].norm() * min_norm / coeffs.shape[1] elif min_norm: lora_proj *= coeffs.norm(dim=1).clip(min=min_norm) # can have rounding errors here! coeffs = (torch.linalg.pinv(lora_proj.double()) @ x.double()).float() return lora_proj.detach(), coeffs.detach() @torch.no_grad() def spectral_projection_of_depthmaps(imgs, intrinsics, depthmaps, subsample, cache_path=None, **kw): # recover 3d points core_depth = [] lora_proj = [] for i, img in enumerate(tqdm(imgs)): cache = os.path.join(cache_path, 'lora_depth', hash_md5(img)) if cache_path else None depth, proj = spectral_projection_depth(intrinsics[i], depthmaps[i], subsample, cache_path=cache, **kw) core_depth.append(depth) lora_proj.append(proj) return core_depth, lora_proj def reproj2d(Trf, pts3d): res = (pts3d @ Trf[:3, :3].transpose(-1, -2)) + Trf[:3, 3] clipped_z = res[:, 2:3].clip(min=1e-3) # make sure we don't have nans! uv = res[:, 0:2] / clipped_z return uv.clip(min=-1000, max=2000) def bfs(tree, start_node): order, predecessors = sp.csgraph.breadth_first_order(tree, start_node, directed=False) ranks = np.arange(len(order)) ranks[order] = ranks.copy() return ranks, predecessors def compute_min_spanning_tree(pws): sparse_graph = sp.dok_array(pws.shape) for i, j in pws.nonzero().cpu().tolist(): sparse_graph[i, j] = -float(pws[i, j]) msp = sp.csgraph.minimum_spanning_tree(sparse_graph) # now reorder the oriented edges, starting from the central point ranks1, _ = bfs(msp, 0) ranks2, _ = bfs(msp, ranks1.argmax()) ranks1, _ = bfs(msp, ranks2.argmax()) # this is the point farther from any leaf root = np.minimum(ranks1, ranks2).argmax() # find the ordered list of edges that describe the tree order, predecessors = sp.csgraph.breadth_first_order(msp, root, directed=False) order = order[1:] # root not do not have a predecessor edges = [(predecessors[i], i) for i in order] return root, edges def show_reconstruction(shapes_or_imgs, K, cam2w, pts3d, gt_cam2w=None, gt_K=None, cam_size=None, masks=None, **kw): viz = SceneViz() cc = cam2w[:, :3, 3] cs = cam_size or float(torch.cdist(cc, cc).fill_diagonal_(np.inf).min(dim=0).values.median()) colors = 64 + np.random.randint(255 - 64, size=(len(cam2w), 3)) if isinstance(shapes_or_imgs, np.ndarray) and shapes_or_imgs.ndim == 2: cam_kws = dict(imsizes=shapes_or_imgs[:, ::-1], cam_size=cs) else: imgs = shapes_or_imgs cam_kws = dict(images=imgs, cam_size=cs) if K is not None: viz.add_cameras(to_numpy(cam2w), to_numpy(K), colors=colors, **cam_kws) if gt_cam2w is not None: if gt_K is None: gt_K = K viz.add_cameras(to_numpy(gt_cam2w), to_numpy(gt_K), colors=colors, marker='o', **cam_kws) if pts3d is not None: for i, p in enumerate(pts3d): if not len(p): continue if masks is None: viz.add_pointcloud(to_numpy(p), color=tuple(colors[i].tolist())) else: viz.add_pointcloud(to_numpy(p), mask=masks[i], color=imgs[i]) viz.show(**kw)