def spvs_coarse(data: dict[str, Any], config: dict[str, Any]) -> None:
    """Perform coarse supervision.

    Update:
        data (dict): {
            "conf_matrix_gt": [N, hw0, hw1],
            'spv_b_ids': [M]
            'spv_i_ids': [M]
            'spv_j_ids': [M]
            'spv_w_pt0_i': [N, hw0, 2], in original image resolution
            'spv_pt1_i': [N, hw1, 2], in original image resolution
        }

    Note:
        - for scannet dataset, there're 3 kinds of resolution {i, c, f}
        - for megadepth dataset, there're 4 kinds of resolution {i, i_resize, c, f}

    """
    # 1. misc
    device = data["image0"].device
    N, _, H0, W0 = data["image0"].shape
    _, _, H1, W1 = data["image1"].shape
    scale = config["LOFTR"]["RESOLUTION"][0]
    scale0 = scale * data["scale0"][:, None] if "scale0" in data else scale
    scale1 = scale * data["scale1"][:, None] if "scale0" in data else scale
    h0, w0, h1, w1 = (x // scale for x in [H0, W0, H1, W1])

    # 2. warp grids
    # create kpts in meshgrid and resize them to image resolution
    grid_pt0_c = create_meshgrid(h0, w0, False, device).reshape(1, h0 * w0, 2).expand(N, h0 * w0, 2)  # [N, hw, 2]
    grid_pt0_i = scale0 * grid_pt0_c
    grid_pt1_c = create_meshgrid(h1, w1, False, device).reshape(1, h1 * w1, 2).expand(N, h1 * w1, 2)
    grid_pt1_i = scale1 * grid_pt1_c

    # mask padded region to (0, 0), so no need to manually mask conf_matrix_gt
    if "mask0" in data:
        grid_pt0_i = mask_pts_at_padded_regions(grid_pt0_i, data["mask0"])
        grid_pt1_i = mask_pts_at_padded_regions(grid_pt1_i, data["mask1"])

    # warp kpts bi-directionally and resize them to coarse-level resolution
    # (no depth consistency check, since it leads to worse results experimentally)
    # (unhandled edge case: points with 0-depth will be warped to the left-up corner)
    _, w_pt0_i = warp_kpts(grid_pt0_i, data["depth0"], data["depth1"], data["T_0to1"], data["K0"], data["K1"])
    _, w_pt1_i = warp_kpts(grid_pt1_i, data["depth1"], data["depth0"], data["T_1to0"], data["K1"], data["K0"])
    w_pt0_c = w_pt0_i / scale1
    w_pt1_c = w_pt1_i / scale0

    # 3. check if mutual nearest neighbor
    w_pt0_c_round = w_pt0_c[:, :, :].round().long()
    nearest_index1 = w_pt0_c_round[..., 0] + w_pt0_c_round[..., 1] * w1
    w_pt1_c_round = w_pt1_c[:, :, :].round().long()
    nearest_index0 = w_pt1_c_round[..., 0] + w_pt1_c_round[..., 1] * w0

    # corner case: out of boundary
    def out_bound_mask(pt: Tensor, w: Tensor, h: Tensor) -> Tensor:
        return (pt[..., 0] < 0) + (pt[..., 0] >= w) + (pt[..., 1] < 0) + (pt[..., 1] >= h)

    nearest_index1[out_bound_mask(w_pt0_c_round, w1, h1)] = 0
    nearest_index0[out_bound_mask(w_pt1_c_round, w0, h0)] = 0

    loop_back = torch.stack([nearest_index0[_b][_i] for _b, _i in enumerate(nearest_index1)], dim=0)
    correct_0to1 = loop_back == torch.arange(h0 * w0, device=device)[None].repeat(N, 1)
    correct_0to1[:, 0] = False  # ignore the top-left corner

    # 4. construct a gt conf_matrix
    conf_matrix_gt = torch.zeros(N, h0 * w0, h1 * w1, device=device)
    b_ids, i_ids = torch.where(correct_0to1 != 0)
    j_ids = nearest_index1[b_ids, i_ids]

    conf_matrix_gt[b_ids, i_ids, j_ids] = 1
    data.update({"conf_matrix_gt": conf_matrix_gt})

    # 5. save coarse matches(gt) for training fine level
    if len(b_ids) == 0:
        # this won't affect fine-level loss calculation
        b_ids = torch.tensor([0], device=device)
        i_ids = torch.tensor([0], device=device)
        j_ids = torch.tensor([0], device=device)

    data.update({"spv_b_ids": b_ids, "spv_i_ids": i_ids, "spv_j_ids": j_ids})

    # 6. save intermediate results (for fast fine-level computation)
    data.update({"spv_w_pt0_i": w_pt0_i, "spv_pt1_i": grid_pt1_i})
Perform coarse supervision.

    Update:
        data (dict): {
            "conf_matrix_gt": [N, hw0, hw1],
            'spv_b_ids': [M]
            'spv_i_ids': [M]
            'spv_j_ids': [M]
            'spv_w_pt0_i': [N, hw0, 2], in original image resolution
            'spv_pt1_i': [N, hw1, 2], in original image resolution
        }

    Note:
        - for scannet dataset, there're 3 kinds of resolution {i, c, f}
        - for megadepth dataset, there're 4 kinds of resolution {i, i_resize, c, f}

    
kornia/feature/loftr/utils/supervision.py