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Object extraction and manipulation primitives for ARC-AGI tasks.
Provides connected-component extraction, color-based splitting,
list reduction (largest/smallest/most_common), spatial queries,
and composition operations (overlay/paint/underpaint).
"""
import numpy as np
from collections import Counter, deque
# ---------------------------------------------------------------------------
# Connected component extraction
# ---------------------------------------------------------------------------
def _flood_fill(grid, start, visited, connectivity=4, univalued=True):
"""BFS flood fill from start. Returns set of (color, (r, c)) cells."""
h, w = grid.shape
r0, c0 = start
seed_color = int(grid[r0, c0])
comp = set()
queue = deque([(r0, c0)])
visited[r0, c0] = True
if connectivity == 8:
deltas = [(-1,-1),(-1,0),(-1,1),(0,-1),(0,1),(1,-1),(1,0),(1,1)]
else:
deltas = [(-1,0),(1,0),(0,-1),(0,1)]
while queue:
r, c = queue.popleft()
val = int(grid[r, c])
if univalued and val != seed_color:
continue
comp.add((val, (r, c)))
for dr, dc in deltas:
nr, nc = r + dr, c + dc
if 0 <= nr < h and 0 <= nc < w and not visited[nr, nc]:
nval = int(grid[nr, nc])
if univalued:
if nval == seed_color:
visited[nr, nc] = True
queue.append((nr, nc))
else:
visited[nr, nc] = True
queue.append((nr, nc))
return comp
def extract_objects(grid, univalued=True, connectivity=4, without_bg=True):
"""Extract connected components from grid.
Args:
grid: 2D numpy array (int)
univalued: if True, each component is single-color
connectivity: 4 or 8
without_bg: if True, skip the most common color (background)
Returns:
list of objects, each object is a set of (color, (row, col))
sorted by size descending
"""
grid = np.array(grid, dtype=int)
h, w = grid.shape
bg = most_common_color(grid) if without_bg else -1
visited = np.zeros((h, w), dtype=bool)
objects = []
for r in range(h):
for c in range(w):
if visited[r, c]:
continue
val = int(grid[r, c])
if val == bg:
visited[r, c] = True
continue
comp = _flood_fill(grid, (r, c), visited, connectivity, univalued)
if comp:
objects.append(comp)
objects.sort(key=len, reverse=True)
return objects
def split_by_color(grid, without_bg=True):
"""Split grid into per-color masks. Returns list of (color, grid) pairs
where each grid has only that color's pixels (rest = 0)."""
grid = np.array(grid, dtype=int)
bg = most_common_color(grid) if without_bg else -1
colors = sorted(set(grid.flatten()) - {bg})
result = []
for c in colors:
mask_grid = np.zeros_like(grid)
mask_grid[grid == c] = c
result.append((c, mask_grid))
return result
# ---------------------------------------------------------------------------
# Object to grid conversion
# ---------------------------------------------------------------------------
def object_to_grid(obj, shape, bg=0):
"""Render an object (set of (color, (r,c))) onto a grid of given shape."""
grid = np.full(shape, bg, dtype=int)
for color, (r, c) in obj:
if 0 <= r < shape[0] and 0 <= c < shape[1]:
grid[r, c] = color
return grid
def object_to_cropped_grid(obj, bg=0):
"""Render object cropped to its bounding box."""
if not obj:
return np.array([[bg]], dtype=int)
rows = [r for _, (r, c) in obj]
cols = [c for _, (r, c) in obj]
rmin, rmax = min(rows), max(rows)
cmin, cmax = min(cols), max(cols)
h, w = rmax - rmin + 1, cmax - cmin + 1
grid = np.full((h, w), bg, dtype=int)
for color, (r, c) in obj:
grid[r - rmin, c - cmin] = color
return grid
def normalize_object(obj):
"""Shift object so its top-left corner is at (0, 0)."""
if not obj:
return obj
rows = [r for _, (r, c) in obj]
cols = [c for _, (r, c) in obj]
rmin, cmin = min(rows), min(cols)
return {(color, (r - rmin, c - cmin)) for color, (r, c) in obj}
def shift_object(obj, dr, dc):
"""Shift all cells by (dr, dc)."""
return {(color, (r + dr, c + dc)) for color, (r, c) in obj}
# ---------------------------------------------------------------------------
# Object queries
# ---------------------------------------------------------------------------
def object_color(obj):
"""Color of a univalued object."""
colors = {c for c, _ in obj}
if len(colors) == 1:
return colors.pop()
return max(colors, key=lambda c: sum(1 for cc, _ in obj if cc == c))
def object_size(obj):
return len(obj)
def object_bbox(obj):
"""Returns (rmin, cmin, rmax, cmax)."""
rows = [r for _, (r, c) in obj]
cols = [c for _, (r, c) in obj]
return min(rows), min(cols), max(rows), max(cols)
def object_height(obj):
rmin, _, rmax, _ = object_bbox(obj)
return rmax - rmin + 1
def object_width(obj):
_, cmin, _, cmax = object_bbox(obj)
return cmax - cmin + 1
def object_center(obj):
rows = [r for _, (r, c) in obj]
cols = [c for _, (r, c) in obj]
return (sum(rows) / len(rows), sum(cols) / len(cols))
# ---------------------------------------------------------------------------
# List reducers
# ---------------------------------------------------------------------------
def largest_object(objects):
"""Return the largest object by cell count."""
return max(objects, key=len) if objects else None
def smallest_object(objects):
"""Return the smallest object by cell count."""
return min(objects, key=len) if objects else None
def most_common_object(objects):
"""Return the object whose normalized shape appears most frequently."""
if not objects:
return None
normed = [frozenset(normalize_object(o)) for o in objects]
counter = Counter(normed)
most_common_shape = counter.most_common(1)[0][0]
for o, n in zip(objects, normed):
if n == most_common_shape:
return o
return objects[0]
def unique_object(objects):
"""If exactly one unique normalized shape exists, return it. Else None."""
normed = [frozenset(normalize_object(o)) for o in objects]
counter = Counter(normed)
uniques = [shape for shape, count in counter.items() if count == 1]
if len(uniques) == 1:
for o, n in zip(objects, normed):
if n == uniques[0]:
return o
return None
def filter_by_color(objects, color):
"""Keep only objects of the given color."""
return [o for o in objects if object_color(o) == color]
def filter_by_size(objects, size):
"""Keep only objects of the given size."""
return [o for o in objects if len(o) == size]
# ---------------------------------------------------------------------------
# Color utilities
# ---------------------------------------------------------------------------
def most_common_color(grid):
"""Most frequent color in the grid (= background)."""
grid = np.array(grid, dtype=int)
counts = Counter(grid.flatten().tolist())
return counts.most_common(1)[0][0]
def least_common_color(grid):
"""Least frequent color in the grid."""
grid = np.array(grid, dtype=int)
counts = Counter(grid.flatten().tolist())
return counts.most_common()[-1][0]
def palette(grid):
"""Set of all colors in grid."""
return set(np.array(grid, dtype=int).flatten().tolist())
def color_normalize(grid):
"""Remap colors by frequency: most common -> 0, next -> 1, etc."""
grid = np.array(grid, dtype=int)
counts = Counter(grid.flatten().tolist())
ranked = [c for c, _ in counts.most_common()]
remap = {c: i for i, c in enumerate(ranked)}
return np.vectorize(remap.get)(grid)
# ---------------------------------------------------------------------------
# Composition / overlay
# ---------------------------------------------------------------------------
def paint(grid, obj):
"""Paint object onto grid. Object cells OVERWRITE grid cells."""
result = np.array(grid, dtype=int).copy()
for color, (r, c) in obj:
if 0 <= r < result.shape[0] and 0 <= c < result.shape[1]:
result[r, c] = color
return result
def underpaint(grid, obj):
"""Paint object onto grid, but ONLY where grid has background color."""
result = np.array(grid, dtype=int).copy()
bg = most_common_color(result)
for color, (r, c) in obj:
if 0 <= r < result.shape[0] and 0 <= c < result.shape[1]:
if result[r, c] == bg:
result[r, c] = color
return result
def overlay_grids(base, foreground):
"""Overlay foreground onto base. Foreground non-zero pixels overwrite."""
base = np.array(base, dtype=int).copy()
fg = np.array(foreground, dtype=int)
h = min(base.shape[0], fg.shape[0])
w = min(base.shape[1], fg.shape[1])
mask = fg[:h, :w] != 0
base[:h, :w][mask] = fg[:h, :w][mask]
return base
def cover(grid, obj):
"""Erase object from grid (replace with background color)."""
result = np.array(grid, dtype=int).copy()
bg = most_common_color(result)
for _, (r, c) in obj:
if 0 <= r < result.shape[0] and 0 <= c < result.shape[1]:
result[r, c] = bg
return result
def canvas(bg_color, shape):
"""Create a blank grid filled with bg_color."""
return np.full(shape, bg_color, dtype=int)
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