Source code for kornia.feature.laf

import math
from typing import Optional, Union

import torch
import torch.nn.functional as F

from kornia.core import Tensor, concatenate, stack, tensor, zeros
from kornia.geometry.conversions import angle_to_rotation_matrix, convert_points_from_homogeneous, rad2deg
from kornia.geometry.linalg import transform_points
from kornia.geometry.transform import pyrdown
from kornia.testing import KORNIA_CHECK_LAF, KORNIA_CHECK_SHAPE


[docs]def get_laf_scale(LAF: Tensor) -> Tensor: """Return a scale of the LAFs. Args: LAF: tensor [BxNx2x3] or [BxNx2x2]. Returns: tensor BxNx1x1. Shape: - Input: :math: `(B, N, 2, 3)` - Output: :math: `(B, N, 1, 1)` Example: >>> input = torch.ones(1, 5, 2, 3) # BxNx2x3 >>> output = get_laf_scale(input) # BxNx1x1 """ KORNIA_CHECK_LAF(LAF) eps = 1e-10 out = LAF[..., 0:1, 0:1] * LAF[..., 1:2, 1:2] - LAF[..., 1:2, 0:1] * LAF[..., 0:1, 1:2] + eps return out.abs().sqrt()
[docs]def get_laf_center(LAF: Tensor) -> Tensor: """Return a center (keypoint) of the LAFs. Args: LAF: tensor [BxNx2x3]. Returns: tensor BxNx2. Shape: - Input: :math: `(B, N, 2, 3)` - Output: :math: `(B, N, 2)` Example: >>> input = torch.ones(1, 5, 2, 3) # BxNx2x3 >>> output = get_laf_center(input) # BxNx2 """ KORNIA_CHECK_LAF(LAF) out = LAF[..., 2] return out
[docs]def get_laf_orientation(LAF: Tensor) -> Tensor: """Return orientation of the LAFs, in degrees. Args: LAF: (Tensor): tensor [BxNx2x3]. Returns: Tensor: tensor BxNx1 . Shape: - Input: :math: `(B, N, 2, 3)` - Output: :math: `(B, N, 1)` Example: >>> input = torch.ones(1, 5, 2, 3) # BxNx2x3 >>> output = get_laf_orientation(input) # BxNx1 """ KORNIA_CHECK_LAF(LAF) angle_rad = torch.atan2(LAF[..., 0, 1], LAF[..., 0, 0]) return rad2deg(angle_rad).unsqueeze(-1)
def set_laf_orientation(LAF: Tensor, angles_degrees: Tensor) -> Tensor: """Change the orientation of the LAFs. Args: LAF: tensor [BxNx2x3]. angles: tensor BxNx1, in degrees. Returns: tensor [BxNx2x3]. Shape: - Input: :math: `(B, N, 2, 3)`, `(B, N, 1)` - Output: :math: `(B, N, 2, 3)` """ KORNIA_CHECK_LAF(LAF) B, N = LAF.shape[:2] rotmat = angle_to_rotation_matrix(angles_degrees).view(B * N, 2, 2) laf_out = concatenate( [torch.bmm(make_upright(LAF).view(B * N, 2, 3)[:, :2, :2], rotmat), LAF.view(B * N, 2, 3)[:, :2, 2:]], dim=2 ).view(B, N, 2, 3) return laf_out
[docs]def laf_from_center_scale_ori(xy: Tensor, scale: Optional[Tensor] = None, ori: Optional[Tensor] = None) -> Tensor: """Return orientation of the LAFs, in radians. Useful to create kornia LAFs from OpenCV keypoints. Args: xy: tensor [BxNx2]. scale: tensor [BxNx1x1]. If not provided, scale = 1 is assumed ori: tensor [BxNx1]. If not provided orientation = 0 is assumed Returns: tensor BxNx2x3. """ KORNIA_CHECK_SHAPE(xy, ["B", "N", "2"]) device = xy.device dtype = xy.dtype B, N = xy.shape[:2] if scale is None: scale = torch.ones(B, N, 1, 1, device=device, dtype=dtype) if ori is None: ori = zeros(B, N, 1, device=device, dtype=dtype) KORNIA_CHECK_SHAPE(scale, ["B", "N", "1", "1"]) KORNIA_CHECK_SHAPE(ori, ["B", "N", "1"]) unscaled_laf = concatenate([angle_to_rotation_matrix(ori.squeeze(-1)), xy.unsqueeze(-1)], dim=-1) laf = scale_laf(unscaled_laf, scale) return laf
[docs]def scale_laf(laf: Tensor, scale_coef: Union[float, Tensor]) -> Tensor: """Multiplies region part of LAF ([:, :, :2, :2]) by a scale_coefficient. So the center, shape and orientation of the local feature stays the same, but the region area changes. Args: laf: tensor [BxNx2x3] or [BxNx2x2]. scale_coef: broadcastable tensor or float. Returns: tensor BxNx2x3. Shape: - Input: :math:`(B, N, 2, 3)` - Input: :math:`(B, N,)` or () - Output: :math:`(B, N, 1, 1)` Example: >>> input = torch.ones(1, 5, 2, 3) # BxNx2x3 >>> scale = 0.5 >>> output = scale_laf(input, scale) # BxNx2x3 """ if (type(scale_coef) is not float) and (type(scale_coef) is not Tensor): raise TypeError("scale_coef should be float or Tensor " "Got {}".format(type(scale_coef))) KORNIA_CHECK_LAF(laf) centerless_laf = laf[:, :, :2, :2] return concatenate([scale_coef * centerless_laf, laf[:, :, :, 2:]], dim=3)
[docs]def make_upright(laf: Tensor, eps: float = 1e-9) -> Tensor: """Rectify the affine matrix, so that it becomes upright. Args: laf: tensor of LAFs. eps : for safe division. Returns: tensor of same shape. Shape: - Input: :math:`(B, N, 2, 3)` - Output: :math:`(B, N, 2, 3)` Example: >>> input = torch.ones(1, 5, 2, 3) # BxNx2x3 >>> output = make_upright(input) # BxNx2x3 """ KORNIA_CHECK_LAF(laf) det = get_laf_scale(laf) scale = det # The function is equivalent to doing 2x2 SVD and resetting rotation # matrix to an identity: U, S, V = svd(LAF); LAF_upright = U * S. b2a2 = torch.sqrt(laf[..., 0:1, 1:2] ** 2 + laf[..., 0:1, 0:1] ** 2) + eps laf1_ell = concatenate([(b2a2 / det).contiguous(), torch.zeros_like(det)], dim=3) laf2_ell = concatenate( [ ((laf[..., 1:2, 1:2] * laf[..., 0:1, 1:2] + laf[..., 1:2, 0:1] * laf[..., 0:1, 0:1]) / (b2a2 * det)), (det / b2a2).contiguous(), ], dim=3, ) laf_unit_scale = concatenate([concatenate([laf1_ell, laf2_ell], dim=2), laf[..., :, 2:3]], dim=3) return scale_laf(laf_unit_scale, scale)
[docs]def ellipse_to_laf(ells: Tensor) -> Tensor: """Convert ellipse regions to LAF format. Ellipse (a, b, c) and upright covariance matrix [a11 a12; 0 a22] are connected by inverse matrix square root: A = invsqrt([a b; b c]). See also https://github.com/vlfeat/vlfeat/blob/master/toolbox/sift/vl_frame2oell.m Args: ells: tensor of ellipses in Oxford format [x y a b c]. Returns: tensor of ellipses in LAF format. Shape: - Input: :math:`(B, N, 5)` - Output: :math:`(B, N, 2, 3)` Example: >>> input = torch.ones(1, 10, 5) # BxNx5 >>> output = ellipse_to_laf(input) # BxNx2x3 """ n_dims = len(ells.size()) if n_dims != 3: raise TypeError("ellipse shape should be must be [BxNx5]. " "Got {}".format(ells.size())) B, N, dim = ells.size() if dim != 5: raise TypeError("ellipse shape should be must be [BxNx5]. " "Got {}".format(ells.size())) # Previous implementation was incorrectly using Cholesky decomp as matrix sqrt # ell_shape = concatenate([concatenate([ells[..., 2:3], ells[..., 3:4]], dim=2).unsqueeze(2), # concatenate([ells[..., 3:4], ells[..., 4:5]], dim=2).unsqueeze(2)], dim=2).view(-1, 2, 2) # out = torch.matrix_power(torch.cholesky(ell_shape, False), -1).view(B, N, 2, 2) # We will calculate 2x2 matrix square root via special case formula # https://en.wikipedia.org/wiki/Square_root_of_a_matrix # "The Cholesky factorization provides another particular example of square root # which should not be confused with the unique non-negative square root." # https://en.wikipedia.org/wiki/Square_root_of_a_2_by_2_matrix # M = (A 0; C D) # R = (sqrt(A) 0; C / (sqrt(A)+sqrt(D)) sqrt(D)) a11 = ells[..., 2:3].abs().sqrt() a12 = torch.zeros_like(a11) a22 = ells[..., 4:5].abs().sqrt() a21 = ells[..., 3:4] / (a11 + a22).clamp(1e-9) A = stack([a11, a12, a21, a22], dim=-1).view(B, N, 2, 2).inverse() out = concatenate([A, ells[..., :2].view(B, N, 2, 1)], dim=3) return out
[docs]def laf_to_boundary_points(LAF: Tensor, n_pts: int = 50) -> Tensor: """Convert LAFs to boundary points of the regions + center. Used for local features visualization, see visualize_laf function. Args: LAF: n_pts: number of points to output. Returns: tensor of boundary points. Shape: - Input: :math:`(B, N, 2, 3)` - Output: :math:`(B, N, n_pts, 2)` """ KORNIA_CHECK_LAF(LAF) B, N, _, _ = LAF.size() pts = concatenate( [ torch.sin(torch.linspace(0, 2 * math.pi, n_pts - 1)).unsqueeze(-1), torch.cos(torch.linspace(0, 2 * math.pi, n_pts - 1)).unsqueeze(-1), torch.ones(n_pts - 1, 1), ], dim=1, ) # Add origin to draw also the orientation pts = concatenate([tensor([0.0, 0.0, 1.0]).view(1, 3), pts], dim=0).unsqueeze(0).expand(B * N, n_pts, 3) pts = pts.to(LAF.device).to(LAF.dtype) aux = tensor([0.0, 0.0, 1.0]).view(1, 1, 3).expand(B * N, 1, 3) HLAF = concatenate([LAF.view(-1, 2, 3), aux.to(LAF.device).to(LAF.dtype)], dim=1) pts_h = torch.bmm(HLAF, pts.permute(0, 2, 1)).permute(0, 2, 1) return convert_points_from_homogeneous(pts_h.view(B, N, n_pts, 3))
def get_laf_pts_to_draw(LAF: Tensor, img_idx: int = 0): """Return numpy array for drawing LAFs (local features). Args: LAF: n_pts: number of boundary points to output. Returns: tensor of boundary points. Shape: - Input: :math:`(B, N, 2, 3)` - Output: :math:`(B, N, n_pts, 2)` Examples: x, y = get_laf_pts_to_draw(LAF, img_idx) plt.figure() plt.imshow(kornia.utils.tensor_to_image(img[img_idx])) plt.plot(x, y, 'r') plt.show() """ # TODO: Refactor doctest KORNIA_CHECK_LAF(LAF) pts = laf_to_boundary_points(LAF[img_idx : img_idx + 1])[0] pts_np = pts.detach().permute(1, 0, 2).cpu().numpy() return (pts_np[..., 0], pts_np[..., 1])
[docs]def denormalize_laf(LAF: Tensor, images: Tensor) -> Tensor: """De-normalize LAFs from scale to image scale. B,N,H,W = images.size() MIN_SIZE = min(H,W) [a11 a21 x] [a21 a22 y] becomes [a11*MIN_SIZE a21*MIN_SIZE x*W] [a21*MIN_SIZE a22*MIN_SIZE y*H] Args: LAF: images: images, LAFs are detected in. Returns: the denormalized lafs. Shape: - Input: :math:`(B, N, 2, 3)` - Output: :math:`(B, N, 2, 3)` """ KORNIA_CHECK_LAF(LAF) _, _, h, w = images.size() wf = float(w) hf = float(h) min_size = min(hf, wf) coef = torch.ones(1, 1, 2, 3).to(LAF.dtype).to(LAF.device) * min_size coef[0, 0, 0, 2] = wf coef[0, 0, 1, 2] = hf return coef.expand_as(LAF) * LAF
[docs]def normalize_laf(LAF: Tensor, images: Tensor) -> Tensor: """Normalize LAFs to [0,1] scale from pixel scale. See below: B,N,H,W = images.size() MIN_SIZE = min(H,W) [a11 a21 x] [a21 a22 y] becomes: [a11/MIN_SIZE a21/MIN_SIZE x/W] [a21/MIN_SIZE a22/MIN_SIZE y/H] Args: LAF: (Tensor). images: (Tensor) images, LAFs are detected in Returns: LAF: (Tensor). Shape: - Input: :math:`(B, N, 2, 3)` - Output: :math:`(B, N, 2, 3)` """ KORNIA_CHECK_LAF(LAF) _, _, h, w = images.size() wf = float(w) hf = float(h) min_size = min(hf, wf) coef = torch.ones(1, 1, 2, 3).to(LAF.dtype).to(LAF.device) / min_size coef[0, 0, 0, 2] = 1.0 / wf coef[0, 0, 1, 2] = 1.0 / hf return coef.expand_as(LAF) * LAF
def generate_patch_grid_from_normalized_LAF(img: Tensor, LAF: Tensor, PS: int = 32) -> Tensor: """Helper function for affine grid generation. Args: img: image tensor of shape :math:`(B, CH, H, W)`. LAF: laf with shape :math:`(B, N, 2, 3)`. PS: patch size to be extracted. Returns: grid """ KORNIA_CHECK_LAF(LAF) B, N, _, _ = LAF.size() _, ch, h, w = img.size() # norm, then renorm is needed for allowing detection on one resolution # and extraction at arbitrary other LAF_renorm = denormalize_laf(LAF, img) grid = F.affine_grid(LAF_renorm.view(B * N, 2, 3), [B * N, ch, PS, PS], align_corners=False) grid[..., :, 0] = 2.0 * grid[..., :, 0].clone() / float(w) - 1.0 grid[..., :, 1] = 2.0 * grid[..., :, 1].clone() / float(h) - 1.0 return grid
[docs]def extract_patches_simple( img: Tensor, laf: Tensor, PS: int = 32, normalize_lafs_before_extraction: bool = True ) -> Tensor: """Extract patches defined by LAFs from image tensor. No smoothing applied, huge aliasing (better use extract_patches_from_pyramid). Args: img: images, LAFs are detected in. laf: PS: patch size. normalize_lafs_before_extraction: if True, lafs are normalized to image size. Returns: patches with shape :math:`(B, N, CH, PS,PS)`. """ KORNIA_CHECK_LAF(laf) if normalize_lafs_before_extraction: nlaf = normalize_laf(laf, img) else: nlaf = laf _, ch, h, w = img.size() B, N, _, _ = laf.size() out = [] # for loop temporarily, to be refactored for i in range(B): grid = generate_patch_grid_from_normalized_LAF(img[i : i + 1], nlaf[i : i + 1], PS).to(img.device) out.append( F.grid_sample( img[i : i + 1].expand(grid.size(0), ch, h, w), grid, padding_mode="border", align_corners=False ) ) return concatenate(out, dim=0).view(B, N, ch, PS, PS)
[docs]def extract_patches_from_pyramid( img: Tensor, laf: Tensor, PS: int = 32, normalize_lafs_before_extraction: bool = True ) -> Tensor: """Extract patches defined by LAFs from image tensor. Patches are extracted from appropriate pyramid level. Args: laf: images: images, LAFs are detected in. PS: patch size. normalize_lafs_before_extraction: if True, lafs are normalized to image size. Returns: patches with shape :math:`(B, N, CH, PS,PS)`. """ KORNIA_CHECK_LAF(laf) if normalize_lafs_before_extraction: nlaf = normalize_laf(laf, img) else: nlaf = laf B, N, _, _ = laf.size() _, ch, h, w = img.size() scale = 2.0 * get_laf_scale(denormalize_laf(nlaf, img)) / float(PS) pyr_idx = scale.log2().relu().long() cur_img = img cur_pyr_level = 0 out = zeros(B, N, ch, PS, PS).to(nlaf.dtype).to(nlaf.device) while min(cur_img.size(2), cur_img.size(3)) >= PS: _, ch, h, w = cur_img.size() # for loop temporarily, to be refactored for i in range(B): scale_mask = (pyr_idx[i] == cur_pyr_level).squeeze() if (scale_mask.float().sum()) == 0: continue scale_mask = (scale_mask > 0).view(-1) grid = generate_patch_grid_from_normalized_LAF(cur_img[i : i + 1], nlaf[i : i + 1, scale_mask, :, :], PS) patches = F.grid_sample( cur_img[i : i + 1].expand(grid.size(0), ch, h, w), grid, padding_mode="border", align_corners=False ) out[i].masked_scatter_(scale_mask.view(-1, 1, 1, 1), patches) cur_img = pyrdown(cur_img) cur_pyr_level += 1 return out
[docs]def laf_is_inside_image(laf: Tensor, images: Tensor, border: int = 0) -> Tensor: """Check if the LAF is touching or partly outside the image boundary. Returns the mask of LAFs, which are fully inside the image, i.e. valid. Args: laf: :math:`(B, N, 2, 3)`. images: images, lafs are detected in :math:`(B, CH, H, W)`. border: additional border. Returns: mask with shape :math:`(B, N)`. """ KORNIA_CHECK_LAF(laf) _, _, h, w = images.size() pts = laf_to_boundary_points(laf, 12) good_lafs_mask = ( (pts[..., 0] >= border) * (pts[..., 0] <= w - border) * (pts[..., 1] >= border) * (pts[..., 1] <= h - border) ) good_lafs_mask = good_lafs_mask.min(dim=2)[0] return good_lafs_mask
[docs]def laf_to_three_points(laf: Tensor): """Convert local affine frame(LAF) to alternative representation: coordinates of LAF center, LAF-x unit vector, LAF-y unit vector. Args: laf: :math:`(B, N, 2, 3)`. Returns: threepts :math:`(B, N, 2, 3)`. """ KORNIA_CHECK_LAF(laf) three_pts = stack([laf[..., 2] + laf[..., 0], laf[..., 2] + laf[..., 1], laf[..., 2]], dim=-1) return three_pts
[docs]def laf_from_three_points(threepts: Tensor): """Convert three points to local affine frame. Order is (0,0), (0, 1), (1, 0). Args: threepts: :math:`(B, N, 2, 3)`. Returns: laf :math:`(B, N, 2, 3)`. """ laf = stack([threepts[..., 0] - threepts[..., 2], threepts[..., 1] - threepts[..., 2], threepts[..., 2]], dim=-1) return laf
[docs]def perspective_transform_lafs(trans_01: Tensor, lafs_1: Tensor) -> Tensor: r"""Function that applies perspective transformations to a set of local affine frames (LAFs). Args: trans_01: tensor for perspective transformations of shape :math:`(B, 3, 3)`. lafs_1: tensor of lafs of shape :math:`(B, N, 2, 3)`. Returns: tensor of N-dimensional points of shape :math:`(B, N, 2, 3)`. Examples: >>> rng = torch.manual_seed(0) >>> lafs_1 = torch.rand(2, 4, 2, 3) # BxNx2x3 >>> lafs_1 tensor([[[[0.4963, 0.7682, 0.0885], [0.1320, 0.3074, 0.6341]], <BLANKLINE> [[0.4901, 0.8964, 0.4556], [0.6323, 0.3489, 0.4017]], <BLANKLINE> [[0.0223, 0.1689, 0.2939], [0.5185, 0.6977, 0.8000]], <BLANKLINE> [[0.1610, 0.2823, 0.6816], [0.9152, 0.3971, 0.8742]]], <BLANKLINE> <BLANKLINE> [[[0.4194, 0.5529, 0.9527], [0.0362, 0.1852, 0.3734]], <BLANKLINE> [[0.3051, 0.9320, 0.1759], [0.2698, 0.1507, 0.0317]], <BLANKLINE> [[0.2081, 0.9298, 0.7231], [0.7423, 0.5263, 0.2437]], <BLANKLINE> [[0.5846, 0.0332, 0.1387], [0.2422, 0.8155, 0.7932]]]]) >>> trans_01 = torch.eye(3).repeat(2, 1, 1) # Bx3x3 >>> trans_01.shape torch.Size([2, 3, 3]) >>> lafs_0 = perspective_transform_lafs(trans_01, lafs_1) # BxNx2x3 """ KORNIA_CHECK_LAF(lafs_1) if not torch.is_tensor(trans_01): raise TypeError("Input type is not a Tensor") if not trans_01.device == lafs_1.device: raise TypeError("Tensor must be in the same device") if not trans_01.shape[0] == lafs_1.shape[0]: raise ValueError("Input batch size must be the same for both tensors") if (not (trans_01.shape[-1] == 3)) or (not (trans_01.shape[-2] == 3)): raise ValueError("Transformation should be homography") bs, n, _, _ = lafs_1.size() # First, we convert LAF to points threepts_1 = laf_to_three_points(lafs_1) points_1 = threepts_1.permute(0, 1, 3, 2).reshape(bs, n * 3, 2) # First, transform the points points_0 = transform_points(trans_01, points_1) # Back to LAF format threepts_0 = points_0.view(bs, n, 3, 2).permute(0, 1, 3, 2) return laf_from_three_points(threepts_0)