import math
from typing import Union
import numpy as np
from invokeai.app.invocations.constants import LATENT_SCALE_FACTOR
from invokeai.backend.tiles.utils import TBLR, Tile, paste, seam_blend
def calc_overlap(tiles: list[Tile], num_tiles_x: int, num_tiles_y: int) -> list[Tile]:
"""Calculate and update the overlap of a list of tiles.
Args:
tiles (list[Tile]): The list of tiles describing the locations of the respective `tile_images`.
num_tiles_x: the number of tiles on the x axis.
num_tiles_y: the number of tiles on the y axis.
"""
def get_tile_or_none(idx_y: int, idx_x: int) -> Union[Tile, None]:
if idx_y < 0 or idx_y > num_tiles_y or idx_x < 0 or idx_x > num_tiles_x:
return None
return tiles[idx_y * num_tiles_x + idx_x]
for tile_idx_y in range(num_tiles_y):
for tile_idx_x in range(num_tiles_x):
cur_tile = get_tile_or_none(tile_idx_y, tile_idx_x)
top_neighbor_tile = get_tile_or_none(tile_idx_y - 1, tile_idx_x)
left_neighbor_tile = get_tile_or_none(tile_idx_y, tile_idx_x - 1)
assert cur_tile is not None
# Update cur_tile top-overlap and corresponding top-neighbor bottom-overlap.
if top_neighbor_tile is not None:
cur_tile.overlap.top = max(0, top_neighbor_tile.coords.bottom - cur_tile.coords.top)
top_neighbor_tile.overlap.bottom = cur_tile.overlap.top
# Update cur_tile left-overlap and corresponding left-neighbor right-overlap.
if left_neighbor_tile is not None:
cur_tile.overlap.left = max(0, left_neighbor_tile.coords.right - cur_tile.coords.left)
left_neighbor_tile.overlap.right = cur_tile.overlap.left
return tiles
def calc_tiles_with_overlap(
image_height: int, image_width: int, tile_height: int, tile_width: int, overlap: int = 0
) -> list[Tile]:
"""Calculate the tile coordinates for a given image shape under a simple tiling scheme with overlaps.
Args:
image_height (int): The image height in px.
image_width (int): The image width in px.
tile_height (int): The tile height in px. All tiles will have this height.
tile_width (int): The tile width in px. All tiles will have this width.
overlap (int, optional): The target overlap between adjacent tiles. If the tiles do not evenly cover the image
shape, then the last row/column of tiles will overlap more than this. Defaults to 0.
Returns:
list[Tile]: A list of tiles that cover the image shape. Ordered from left-to-right, top-to-bottom.
"""
assert image_height >= tile_height
assert image_width >= tile_width
assert overlap < tile_height
assert overlap < tile_width
non_overlap_per_tile_height = tile_height - overlap
non_overlap_per_tile_width = tile_width - overlap
num_tiles_y = math.ceil((image_height - overlap) / non_overlap_per_tile_height)
num_tiles_x = math.ceil((image_width - overlap) / non_overlap_per_tile_width)
# tiles[y * num_tiles_x + x] is the tile for the y'th row, x'th column.
tiles: list[Tile] = []
# Calculate tile coordinates. (Ignore overlap values for now.)
for tile_idx_y in range(num_tiles_y):
for tile_idx_x in range(num_tiles_x):
tile = Tile(
coords=TBLR(
top=tile_idx_y * non_overlap_per_tile_height,
bottom=tile_idx_y * non_overlap_per_tile_height + tile_height,
left=tile_idx_x * non_overlap_per_tile_width,
right=tile_idx_x * non_overlap_per_tile_width + tile_width,
),
overlap=TBLR(top=0, bottom=0, left=0, right=0),
)
if tile.coords.bottom > image_height:
# If this tile would go off the bottom of the image, shift it so that it is aligned with the bottom
# of the image.
tile.coords.bottom = image_height
tile.coords.top = image_height - tile_height
if tile.coords.right > image_width:
# If this tile would go off the right edge of the image, shift it so that it is aligned with the
# right edge of the image.
tile.coords.right = image_width
tile.coords.left = image_width - tile_width
tiles.append(tile)
return calc_overlap(tiles, num_tiles_x, num_tiles_y)
def calc_tiles_even_split(
image_height: int, image_width: int, num_tiles_x: int, num_tiles_y: int, overlap: int = 0
) -> list[Tile]:
"""Calculate the tile coordinates for a given image shape with the number of tiles requested.
Args:
image_height (int): The image height in px.
image_width (int): The image width in px.
num_x_tiles (int): The number of tile to split the image into on the X-axis.
num_y_tiles (int): The number of tile to split the image into on the Y-axis.
overlap (int, optional): The overlap between adjacent tiles in pixels. Defaults to 0.
Returns:
list[Tile]: A list of tiles that cover the image shape. Ordered from left-to-right, top-to-bottom.
"""
# Ensure the image is divisible by LATENT_SCALE_FACTOR
if image_width % LATENT_SCALE_FACTOR != 0 or image_height % LATENT_SCALE_FACTOR != 0:
raise ValueError(f"image size (({image_width}, {image_height})) must be divisible by {LATENT_SCALE_FACTOR}")
# Calculate the tile size based on the number of tiles and overlap, and ensure it's divisible by 8 (rounding down)
if num_tiles_x > 1:
# ensure the overlap is not more than the maximum overlap if we only have 1 tile then we dont care about overlap
assert overlap <= image_width - (LATENT_SCALE_FACTOR * (num_tiles_x - 1))
tile_size_x = LATENT_SCALE_FACTOR * math.floor(
((image_width + overlap * (num_tiles_x - 1)) // num_tiles_x) / LATENT_SCALE_FACTOR
)
assert overlap < tile_size_x
else:
tile_size_x = image_width
if num_tiles_y > 1:
# ensure the overlap is not more than the maximum overlap if we only have 1 tile then we dont care about overlap
assert overlap <= image_height - (LATENT_SCALE_FACTOR * (num_tiles_y - 1))
tile_size_y = LATENT_SCALE_FACTOR * math.floor(
((image_height + overlap * (num_tiles_y - 1)) // num_tiles_y) / LATENT_SCALE_FACTOR
)
assert overlap < tile_size_y
else:
tile_size_y = image_height
# tiles[y * num_tiles_x + x] is the tile for the y'th row, x'th column.
tiles: list[Tile] = []
# Calculate tile coordinates. (Ignore overlap values for now.)
for tile_idx_y in range(num_tiles_y):
# Calculate the top and bottom of the row
top = tile_idx_y * (tile_size_y - overlap)
bottom = min(top + tile_size_y, image_height)
# For the last row adjust bottom to be the height of the image
if tile_idx_y == num_tiles_y - 1:
bottom = image_height
for tile_idx_x in range(num_tiles_x):
# Calculate the left & right coordinate of each tile
left = tile_idx_x * (tile_size_x - overlap)
right = min(left + tile_size_x, image_width)
# For the last tile in the row adjust right to be the width of the image
if tile_idx_x == num_tiles_x - 1:
right = image_width
tile = Tile(
coords=TBLR(top=top, bottom=bottom, left=left, right=right),
overlap=TBLR(top=0, bottom=0, left=0, right=0),
)
tiles.append(tile)
return calc_overlap(tiles, num_tiles_x, num_tiles_y)
def calc_tiles_min_overlap(
image_height: int,
image_width: int,
tile_height: int,
tile_width: int,
min_overlap: int = 0,
) -> list[Tile]:
"""Calculate the tile coordinates for a given image shape under a simple tiling scheme with overlaps.
Args:
image_height (int): The image height in px.
image_width (int): The image width in px.
tile_height (int): The tile height in px. All tiles will have this height.
tile_width (int): The tile width in px. All tiles will have this width.
min_overlap (int): The target minimum overlap between adjacent tiles. If the tiles do not evenly cover the image
shape, then the overlap will be spread between the tiles.
Returns:
list[Tile]: A list of tiles that cover the image shape. Ordered from left-to-right, top-to-bottom.
"""
assert min_overlap < tile_height
assert min_overlap < tile_width
# catches the cases when the tile size is larger than the images size and adjusts the tile size
if image_width < tile_width:
tile_width = image_width
if image_height < tile_height:
tile_height = image_height
num_tiles_x = math.ceil((image_width - min_overlap) / (tile_width - min_overlap))
num_tiles_y = math.ceil((image_height - min_overlap) / (tile_height - min_overlap))
# tiles[y * num_tiles_x + x] is the tile for the y'th row, x'th column.
tiles: list[Tile] = []
# Calculate tile coordinates. (Ignore overlap values for now.)
for tile_idx_y in range(num_tiles_y):
top = (tile_idx_y * (image_height - tile_height)) // (num_tiles_y - 1) if num_tiles_y > 1 else 0
bottom = top + tile_height
for tile_idx_x in range(num_tiles_x):
left = (tile_idx_x * (image_width - tile_width)) // (num_tiles_x - 1) if num_tiles_x > 1 else 0
right = left + tile_width
tile = Tile(
coords=TBLR(top=top, bottom=bottom, left=left, right=right),
overlap=TBLR(top=0, bottom=0, left=0, right=0),
)
tiles.append(tile)
return calc_overlap(tiles, num_tiles_x, num_tiles_y)
def merge_tiles_with_linear_blending(
dst_image: np.ndarray, tiles: list[Tile], tile_images: list[np.ndarray], blend_amount: int
):
"""Merge a set of image tiles into `dst_image` with linear blending between the tiles.
We expect every tile edge to either:
1) have an overlap of 0, because it is aligned with the image edge, or
2) have an overlap >= blend_amount.
If neither of these conditions are satisfied, we raise an exception.
The linear blending is centered at the halfway point of the overlap between adjacent tiles.
Args:
dst_image (np.ndarray): The destination image. Shape: (H, W, C).
tiles (list[Tile]): The list of tiles describing the locations of the respective `tile_images`.
tile_images (list[np.ndarray]): The tile images to merge into `dst_image`.
blend_amount (int): The amount of blending (in px) between adjacent overlapping tiles.
"""
# Sort tiles and images first by left x coordinate, then by top y coordinate. During tile processing, we want to
# iterate over tiles left-to-right, top-to-bottom.
tiles_and_images = list(zip(tiles, tile_images, strict=True))
tiles_and_images = sorted(tiles_and_images, key=lambda x: x[0].coords.left)
tiles_and_images = sorted(tiles_and_images, key=lambda x: x[0].coords.top)
# Organize tiles into rows.
tile_and_image_rows: list[list[tuple[Tile, np.ndarray]]] = []
cur_tile_and_image_row: list[tuple[Tile, np.ndarray]] = []
first_tile_in_cur_row, _ = tiles_and_images[0]
for tile_and_image in tiles_and_images:
tile, _ = tile_and_image
if not (
tile.coords.top == first_tile_in_cur_row.coords.top
and tile.coords.bottom == first_tile_in_cur_row.coords.bottom
):
# Store the previous row, and start a new one.
tile_and_image_rows.append(cur_tile_and_image_row)
cur_tile_and_image_row = []
first_tile_in_cur_row, _ = tile_and_image
cur_tile_and_image_row.append(tile_and_image)
tile_and_image_rows.append(cur_tile_and_image_row)
# Prepare 1D linear gradients for blending.
gradient_left_x = np.linspace(start=0.0, stop=1.0, num=blend_amount)
gradient_top_y = np.linspace(start=0.0, stop=1.0, num=blend_amount)
# Convert shape: (blend_amount, ) -> (blend_amount, 1). The extra dimension enables the gradient to be applied
# to a 2D image via broadcasting. Note that no additional dimension is needed on gradient_left_x for
# broadcasting to work correctly.
gradient_top_y = np.expand_dims(gradient_top_y, axis=1)
for tile_and_image_row in tile_and_image_rows:
first_tile_in_row, _ = tile_and_image_row[0]
row_height = first_tile_in_row.coords.bottom - first_tile_in_row.coords.top
row_image = np.zeros((row_height, dst_image.shape[1], dst_image.shape[2]), dtype=dst_image.dtype)
# Blend the tiles in the row horizontally.
for tile, tile_image in tile_and_image_row:
# We expect the tiles to be ordered left-to-right. For each tile, we construct a mask that applies linear
# blending to the left of the current tile. The inverse linear blending is automatically applied to the
# right of the tiles that have already been pasted by the paste(...) operation.
tile_height, tile_width, _ = tile_image.shape
mask = np.ones(shape=(tile_height, tile_width), dtype=np.float64)
# Left blending:
if tile.overlap.left > 0:
assert tile.overlap.left >= blend_amount
# Center the blending gradient in the middle of the overlap.
blend_start_left = tile.overlap.left // 2 - blend_amount // 2
# The region left of the blending region is masked completely.
mask[:, :blend_start_left] = 0.0
# Apply the blend gradient to the mask.
mask[:, blend_start_left : blend_start_left + blend_amount] = gradient_left_x
# For visual debugging:
# tile_image[:, blend_start_left : blend_start_left + blend_amount] = 0
paste(
dst_image=row_image,
src_image=tile_image,
box=TBLR(
top=0, bottom=tile.coords.bottom - tile.coords.top, left=tile.coords.left, right=tile.coords.right
),
mask=mask,
)
# Blend the row into the dst_image vertically.
# We construct a mask that applies linear blending to the top of the current row. The inverse linear blending is
# automatically applied to the bottom of the tiles that have already been pasted by the paste(...) operation.
mask = np.ones(shape=(row_image.shape[0], row_image.shape[1]), dtype=np.float64)
# Top blending:
# (See comments under 'Left blending' for an explanation of the logic.)
# We assume that the entire row has the same vertical overlaps as the first_tile_in_row.
if first_tile_in_row.overlap.top > 0:
assert first_tile_in_row.overlap.top >= blend_amount
blend_start_top = first_tile_in_row.overlap.top // 2 - blend_amount // 2
mask[:blend_start_top, :] = 0.0
mask[blend_start_top : blend_start_top + blend_amount, :] = gradient_top_y
# For visual debugging:
# row_image[blend_start_top : blend_start_top + blend_amount, :] = 0
paste(
dst_image=dst_image,
src_image=row_image,
box=TBLR(
top=first_tile_in_row.coords.top,
bottom=first_tile_in_row.coords.bottom,
left=0,
right=row_image.shape[1],
),
mask=mask,
)
def merge_tiles_with_seam_blending(
dst_image: np.ndarray, tiles: list[Tile], tile_images: list[np.ndarray], blend_amount: int
):
"""Merge a set of image tiles into `dst_image` with seam blending between the tiles.
We expect every tile edge to either:
1) have an overlap of 0, because it is aligned with the image edge, or
2) have an overlap >= blend_amount.
If neither of these conditions are satisfied, we raise an exception.
The seam blending is centered on a seam of least energy of the overlap between adjacent tiles.
Args:
dst_image (np.ndarray): The destination image. Shape: (H, W, C).
tiles (list[Tile]): The list of tiles describing the locations of the respective `tile_images`.
tile_images (list[np.ndarray]): The tile images to merge into `dst_image`.
blend_amount (int): The amount of blending (in px) between adjacent overlapping tiles.
"""
# Sort tiles and images first by left x coordinate, then by top y coordinate. During tile processing, we want to
# iterate over tiles left-to-right, top-to-bottom.
tiles_and_images = list(zip(tiles, tile_images, strict=True))
tiles_and_images = sorted(tiles_and_images, key=lambda x: x[0].coords.left)
tiles_and_images = sorted(tiles_and_images, key=lambda x: x[0].coords.top)
# Organize tiles into rows.
tile_and_image_rows: list[list[tuple[Tile, np.ndarray]]] = []
cur_tile_and_image_row: list[tuple[Tile, np.ndarray]] = []
first_tile_in_cur_row, _ = tiles_and_images[0]
for tile_and_image in tiles_and_images:
tile, _ = tile_and_image
if not (
tile.coords.top == first_tile_in_cur_row.coords.top
and tile.coords.bottom == first_tile_in_cur_row.coords.bottom
):
# Store the previous row, and start a new one.
tile_and_image_rows.append(cur_tile_and_image_row)
cur_tile_and_image_row = []
first_tile_in_cur_row, _ = tile_and_image
cur_tile_and_image_row.append(tile_and_image)
tile_and_image_rows.append(cur_tile_and_image_row)
for tile_and_image_row in tile_and_image_rows:
first_tile_in_row, _ = tile_and_image_row[0]
row_height = first_tile_in_row.coords.bottom - first_tile_in_row.coords.top
row_image = np.zeros((row_height, dst_image.shape[1], dst_image.shape[2]), dtype=dst_image.dtype)
# Blend the tiles in the row horizontally.
for tile, tile_image in tile_and_image_row:
# We expect the tiles to be ordered left-to-right.
# For each tile:
# - extract the overlap regions and pass to seam_blend()
# - apply blended region to the row_image
# - apply the un-blended region to the row_image
tile_height, tile_width, _ = tile_image.shape
overlap_size = tile.overlap.left
# Left blending:
if overlap_size > 0:
assert overlap_size >= blend_amount
overlap_coord_right = tile.coords.left + overlap_size
src_overlap = row_image[:, tile.coords.left : overlap_coord_right]
dst_overlap = tile_image[:, :overlap_size]
blended_overlap = seam_blend(src_overlap, dst_overlap, blend_amount, x_seam=False)
row_image[:, tile.coords.left : overlap_coord_right] = blended_overlap
row_image[:, overlap_coord_right : tile.coords.right] = tile_image[:, overlap_size:]
else:
# no overlap just paste the tile
row_image[:, tile.coords.left : tile.coords.right] = tile_image
# Blend the row into the dst_image
# We assume that the entire row has the same vertical overlaps as the first_tile_in_row.
# Rows are processed in the same way as tiles (extract overlap, blend, apply)
row_overlap_size = first_tile_in_row.overlap.top
if row_overlap_size > 0:
assert row_overlap_size >= blend_amount
overlap_coords_bottom = first_tile_in_row.coords.top + row_overlap_size
src_overlap = dst_image[first_tile_in_row.coords.top : overlap_coords_bottom, :]
dst_overlap = row_image[:row_overlap_size, :]
blended_overlap = seam_blend(src_overlap, dst_overlap, blend_amount, x_seam=True)
dst_image[first_tile_in_row.coords.top : overlap_coords_bottom, :] = blended_overlap
dst_image[overlap_coords_bottom : first_tile_in_row.coords.bottom, :] = row_image[row_overlap_size:, :]
else:
# no overlap just paste the row
dst_image[first_tile_in_row.coords.top : first_tile_in_row.coords.bottom, :] = row_image