common/utils/transforms.py

import torch
import numpy as np
import scipy
from config import cfg
from torch.nn import functional as F
import torchgeometry as tgm


def cam2pixel(cam_coord, f, c):
    x = cam_coord[:, 0] / cam_coord[:, 2] * f[0] + c[0]
    y = cam_coord[:, 1] / cam_coord[:, 2] * f[1] + c[1]
    z = cam_coord[:, 2]
    return np.stack((x, y, z), 1)


def pixel2cam(pixel_coord, f, c):
    x = (pixel_coord[:, 0] - c[0]) / f[0] * pixel_coord[:, 2]
    y = (pixel_coord[:, 1] - c[1]) / f[1] * pixel_coord[:, 2]
    z = pixel_coord[:, 2]
    return np.stack((x, y, z), 1)


def world2cam(world_coord, R, t):
    cam_coord = np.dot(R, world_coord.transpose(1, 0)).transpose(1, 0) + t.reshape(1, 3)
    return cam_coord


def cam2world(cam_coord, R, t):
    world_coord = np.dot(np.linalg.inv(R), (cam_coord - t.reshape(1, 3)).transpose(1, 0)).transpose(1, 0)
    return world_coord


def rigid_transform_3D(A, B):
    n, dim = A.shape
    centroid_A = np.mean(A, axis=0)
    centroid_B = np.mean(B, axis=0)
    H = np.dot(np.transpose(A - centroid_A), B - centroid_B) / n
    U, s, V = np.linalg.svd(H)
    R = np.dot(np.transpose(V), np.transpose(U))
    if np.linalg.det(R) < 0:
        s[-1] = -s[-1]
        V[2] = -V[2]
        R = np.dot(np.transpose(V), np.transpose(U))

    varP = np.var(A, axis=0).sum()
    c = 1 / varP * np.sum(s)

    t = -np.dot(c * R, np.transpose(centroid_A)) + np.transpose(centroid_B)
    return c, R, t


def rigid_align(A, B):
    c, R, t = rigid_transform_3D(A, B)
    A2 = np.transpose(np.dot(c * R, np.transpose(A))) + t
    return A2


def transform_joint_to_other_db(src_joint, src_name, dst_name):
    src_joint_num = len(src_name)
    dst_joint_num = len(dst_name)

    new_joint = np.zeros(((dst_joint_num,) + src_joint.shape[1:]), dtype=np.float32)
    for src_idx in range(len(src_name)):
        name = src_name[src_idx]
        if name in dst_name:
            dst_idx = dst_name.index(name)
            new_joint[dst_idx] = src_joint[src_idx]

    return new_joint


def rot6d_to_axis_angle(x):
    batch_size = x.shape[0]

    x = x.view(-1, 3, 2)
    a1 = x[:, :, 0]
    a2 = x[:, :, 1]
    b1 = F.normalize(a1)
    b2 = F.normalize(a2 - torch.einsum('bi,bi->b', b1, a2).unsqueeze(-1) * b1)
    b3 = torch.cross(b1, b2)
    rot_mat = torch.stack((b1, b2, b3), dim=-1)  # 3x3 rotation matrix

    rot_mat = torch.cat([rot_mat, torch.zeros((batch_size, 3, 1)).to(cfg.device).float()], 2)  # 3x4 rotation matrix
    axis_angle = tgm.rotation_matrix_to_angle_axis(rot_mat).reshape(-1, 3)  # axis-angle
    axis_angle[torch.isnan(axis_angle)] = 0.0
    return axis_angle


def sample_joint_features(img_feat, joint_xy):
    height, width = img_feat.shape[2:]
    x = joint_xy[:, :, 0] / (width - 1) * 2 - 1
    y = joint_xy[:, :, 1] / (height - 1) * 2 - 1
    grid = torch.stack((x, y), 2)[:, :, None, :]
    img_feat = F.grid_sample(img_feat, grid, align_corners=True)[:, :, :, 0]  # batch_size, channel_dim, joint_num
    img_feat = img_feat.permute(0, 2, 1).contiguous()  # batch_size, joint_num, channel_dim
    return img_feat


def soft_argmax_2d(heatmap2d):
    batch_size = heatmap2d.shape[0]
    height, width = heatmap2d.shape[2:]
    heatmap2d = heatmap2d.reshape((batch_size, -1, height * width))
    heatmap2d = F.softmax(heatmap2d, 2)
    heatmap2d = heatmap2d.reshape((batch_size, -1, height, width))

    accu_x = heatmap2d.sum(dim=(2))
    accu_y = heatmap2d.sum(dim=(3))

    accu_x = accu_x * torch.arange(width).float().to(cfg.device)[None, None, :]
    accu_y = accu_y * torch.arange(height).float().to(cfg.device)[None, None, :]

    accu_x = accu_x.sum(dim=2, keepdim=True)
    accu_y = accu_y.sum(dim=2, keepdim=True)

    coord_out = torch.cat((accu_x, accu_y), dim=2)
    return coord_out


def soft_argmax_3d(heatmap3d):
    batch_size = heatmap3d.shape[0]
    depth, height, width = heatmap3d.shape[2:]
    heatmap3d = heatmap3d.reshape((batch_size, -1, depth * height * width))
    heatmap3d = F.softmax(heatmap3d, 2)
    heatmap3d = heatmap3d.reshape((batch_size, -1, depth, height, width))

    accu_x = heatmap3d.sum(dim=(2, 3))
    accu_y = heatmap3d.sum(dim=(2, 4))
    accu_z = heatmap3d.sum(dim=(3, 4))

    accu_x = accu_x * torch.arange(width).float().to(cfg.device)[None, None, :]
    accu_y = accu_y * torch.arange(height).float().to(cfg.device)[None, None, :]
    accu_z = accu_z * torch.arange(depth).float().to(cfg.device)[None, None, :]

    accu_x = accu_x.sum(dim=2, keepdim=True)
    accu_y = accu_y.sum(dim=2, keepdim=True)
    accu_z = accu_z.sum(dim=2, keepdim=True)

    coord_out = torch.cat((accu_x, accu_y, accu_z), dim=2)
    return coord_out


def restore_bbox(bbox_center, bbox_size, aspect_ratio, extension_ratio):
    bbox = bbox_center.view(-1, 1, 2) + torch.cat((-bbox_size.view(-1, 1, 2) / 2., bbox_size.view(-1, 1, 2) / 2.),
                                                  1)  # xyxy in (cfg.output_hm_shape[2], cfg.output_hm_shape[1]) space
    bbox[:, :, 0] = bbox[:, :, 0] / cfg.output_hm_shape[2] * cfg.input_body_shape[1]
    bbox[:, :, 1] = bbox[:, :, 1] / cfg.output_hm_shape[1] * cfg.input_body_shape[0]
    bbox = bbox.view(-1, 4)

    # xyxy -> xywh
    bbox[:, 2] = bbox[:, 2] - bbox[:, 0]
    bbox[:, 3] = bbox[:, 3] - bbox[:, 1]

    # aspect ratio preserving bbox
    w = bbox[:, 2]
    h = bbox[:, 3]
    c_x = bbox[:, 0] + w / 2.
    c_y = bbox[:, 1] + h / 2.

    mask1 = w > (aspect_ratio * h)
    mask2 = w < (aspect_ratio * h)
    h[mask1] = w[mask1] / aspect_ratio
    w[mask2] = h[mask2] * aspect_ratio

    bbox[:, 2] = w * extension_ratio
    bbox[:, 3] = h * extension_ratio
    bbox[:, 0] = c_x - bbox[:, 2] / 2.
    bbox[:, 1] = c_y - bbox[:, 3] / 2.

    # xywh -> xyxy
    bbox[:, 2] = bbox[:, 2] + bbox[:, 0]
    bbox[:, 3] = bbox[:, 3] + bbox[:, 1]
    return bbox