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Two 2D color fields are shown side by side. Each sample uses a randomly-
chosen colour mode: a scalar 2D multi-scale noise field rendered through
one of several colormaps (viridis / plasma / inferno / magma / cividis /
coolwarm), OR a full-RGB variant where three independent scalar fields are
stacked directly as red, green and blue channels.
Each panel is divided into a 3×3 grid of 9 cells. Independently for each
cell, the right panel may or may not have a radially-faded perturbation
applied at the cell's centre. At the perturbation's rim the right panel
matches the left exactly (seamless), and at the centre its content is
blended toward a freshly-drawn, DC-matched field so only the texture
differs — there is no visible "dot" of uniform offset.
Task: count how many of the 9 cells are identical between the two panels
(i.e. how many cells have NO perturbation). Answer is an integer 0..9.
"""
from __future__ import annotations
import argparse
import json
import random
from pathlib import Path
from typing import Any, Dict, List, Tuple
import matplotlib
matplotlib.use("Agg")
import matplotlib.pyplot as plt
import matplotlib.patches as mpatches
import numpy as np
from tqdm import tqdm
# ---------------------------------------------------------------------------
# Constants
# ---------------------------------------------------------------------------
GRID_N = 3 # 3×3 grid → 9 cells (difficulty-tunable)
CELL_W = 200 # pixels per cell (fixed; panel auto-scales)
CELL_H = 200
PANEL_W = CELL_W * GRID_N # pixels per panel (square field)
PANEL_H = CELL_H * GRID_N
# Radius of the (optional) circular perturbation centred inside each cell.
# Must stay within the cell so perturbations don't cross cell boundaries.
CIRCLE_RADIUS = 70
assert CIRCLE_RADIUS < min(CELL_W, CELL_H) // 2
# Visibility thresholds for the blended-fresh texture inside a perturbed
# cell. Peak and mean |fresh − orig| (after DC-matching) must exceed these
# multiples of the field std; otherwise the fresh field is resampled.
MIN_BLEND_DIFF_MULT = 2.6
MIN_BLEND_MEAN_DIFF_MULT = 1.0
# Frequency scale multiplier on generate_field sigmas (difficulty-tunable).
# Smaller value → finer-grained texture, harder task.
FIELD_FREQUENCY_SCALE = 1.0
# Rendering modes — one is picked at random per sample.
COLOR_MODES: List[str] = [
"viridis", "plasma", "inferno", "magma", "cividis", "coolwarm", "rgb",
]
JITTER_AMPLITUDE = 0.012
BG_COLOR = "#ffffff"
BORDER_COLOR = "#888888"
BORDER_WIDTH = 1.5
GRID_LINE_COLOR = "#ffffff"
GRID_LINE_WIDTH = 1.6
GRID_LINE_ALPHA = 0.85
LABEL_COLOR = "#333333"
HIGHLIGHT_COLOR = "#dc1e1e"
MARGIN_PX = 70
GAP_PX = 90
LABEL_HEIGHT = 44
def _build_question() -> str:
n = GRID_N
total = n * n
return (
f"Three panels are shown side by side. The leftmost panel is an INDEX "
f"key: a {n}×{n} grid whose cells are numbered 1 through {total} in "
f"row-major order (top-left = 1, increasing left-to-right then "
f"top-to-bottom). The middle and right panels are 2D color fields, "
f"each divided into the same {n}×{n} grid by thin white gridlines. "
f"Compare the middle (Field A) and right (Field B) panels cell by "
f"cell. List the numbers of all cells that DIFFER between Field A "
f"and Field B, in ascending order, separated by commas (for example: "
f"\"1, 4, {total}\"). If no cells differ, write \"none\". "
f"Provide your final answer enclosed in <answer>...</answer> tags."
)
QUESTION = (
"Two panels are shown side by side. Each panel is a 2D color field, and "
"each panel is divided into a 3×3 grid of 9 cells by thin white "
"gridlines. Compare the left and right panels cell by cell. Count how "
"many of the 9 cells are DIFFERENT between the two panels. Report the "
"count as an integer between 0 and 9. "
"Provide your final answer enclosed in <answer>...</answer> tags."
)
# ---------------------------------------------------------------------------
# 2D field generator (multi-scale smoothed Gaussian noise)
# ---------------------------------------------------------------------------
def _separable_gaussian_blur(arr: np.ndarray, sigma: float) -> np.ndarray:
"""Apply a separable 2D Gaussian blur via two 1D convolutions."""
max_radius = max(1, min(arr.shape) // 2 - 1)
radius = max(1, min(int(sigma * 4), max_radius))
k = np.arange(-radius, radius + 1, dtype=np.float64)
w = np.exp(-(k * k) / (2.0 * sigma * sigma))
kernel = w / w.sum()
out = np.apply_along_axis(
lambda row: np.convolve(row, kernel, mode="same"), axis=1, arr=arr
)
out = np.apply_along_axis(
lambda col: np.convolve(col, kernel, mode="same"), axis=0, arr=out
)
return out
def _smoothed_noise_2d(
np_rng: np.random.Generator,
shape: Tuple[int, int],
sigma: float,
) -> np.ndarray:
raw = np_rng.standard_normal(size=shape)
return _separable_gaussian_blur(raw, sigma)
def generate_field(
np_rng: np.random.Generator,
shape: Tuple[int, int],
) -> np.ndarray:
"""Arbitrary non-periodic 2D random field built from multi-scale smoothed
Gaussian noise."""
fs = max(0.1, float(FIELD_FREQUENCY_SCALE))
coarse = _smoothed_noise_2d(np_rng, shape, sigma=np_rng.uniform(28.0, 44.0) * fs)
medium = _smoothed_noise_2d(np_rng, shape, sigma=np_rng.uniform(9.0, 16.0) * fs)
fine = _smoothed_noise_2d(np_rng, shape, sigma=np_rng.uniform(2.5, 4.5) * fs)
micro = _smoothed_noise_2d(np_rng, shape, sigma=np_rng.uniform(0.9, 1.4) * fs)
def _norm(a: np.ndarray) -> np.ndarray:
s = float(np.std(a)) or 1.0
return a / s
f = (
1.8 * _norm(coarse)
+ 0.75 * _norm(medium)
+ 0.40 * _norm(fine)
+ 0.20 * _norm(micro)
)
f = f + np_rng.normal(0.0, 0.04, size=shape)
return f
# ---------------------------------------------------------------------------
# Cell geometry and perturbation selection
# ---------------------------------------------------------------------------
def _cell_center(row: int, col: int) -> Tuple[int, int]:
cx = col * CELL_W + CELL_W // 2
cy = row * CELL_H + CELL_H // 2
return cx, cy
MIN_PERTURBED = 0
MAX_PERTURBED = GRID_N * GRID_N
def _sample_perturbed_cells(rng: random.Random) -> List[Tuple[int, int]]:
"""Return list of (row, col) cells to perturb. Draws ``num_perturbed``
uniformly from [MIN_PERTURBED..MAX_PERTURBED] then picks that many cells."""
num_perturbed = rng.randint(MIN_PERTURBED, MAX_PERTURBED)
all_cells = [(r, c) for r in range(GRID_N) for c in range(GRID_N)]
rng.shuffle(all_cells)
return sorted(all_cells[:num_perturbed])
# ---------------------------------------------------------------------------
# Radial-fade perturbation (circle-shaped, magnitude fades to zero at rim)
# ---------------------------------------------------------------------------
def _build_disk_mask(radius: int) -> np.ndarray:
"""Smootherstep radial fade mask, exactly 0 at the rim and C²-smooth."""
n = 2 * radius + 1
yy, xx = np.mgrid[0:n, 0:n].astype(np.float64)
c = float(radius)
dist = np.sqrt((xx - c) ** 2 + (yy - c) ** 2)
t = np.clip(dist / float(radius), 0.0, 1.0)
mask = 1.0 - (6.0 * t ** 5 - 15.0 * t ** 4 + 10.0 * t ** 3)
return mask
def _apply_radial_perturbation(
np_rng: np.random.Generator,
left: np.ndarray,
right: np.ndarray,
cx: int,
cy: int,
radius: int,
field_std: float,
max_tries: int = 40,
) -> None:
r = radius
n = 2 * r + 1
y_lo, y_hi = cy - r, cy + r + 1
x_lo, x_hi = cx - r, cx + r + 1
orig = left[y_lo:y_hi, x_lo:x_hi]
mask = _build_disk_mask(r)
min_peak = MIN_BLEND_DIFF_MULT * field_std
min_mean = MIN_BLEND_MEAN_DIFF_MULT * field_std
inner = mask > 0.5
pad_canvas = n + 60
pad_off = (pad_canvas - n) // 2
for _ in range(max_tries):
fresh_full = generate_field(np_rng, shape=(pad_canvas, pad_canvas))
fresh = fresh_full[pad_off:pad_off + n, pad_off:pad_off + n].copy()
# DC-match: remove bulk brightness offset so only texture differs.
fresh = fresh - (float(np.mean(fresh[inner])) - float(np.mean(orig[inner])))
abs_diff = np.abs(fresh[inner] - orig[inner])
if float(np.max(abs_diff)) < min_peak:
continue
if float(np.mean(abs_diff)) < min_mean:
continue
right[y_lo:y_hi, x_lo:x_hi] = (1.0 - mask) * orig + mask * fresh
return
raise RuntimeError("Could not find a sufficiently different fresh field for this cell.")
def build_sample(
rng: random.Random,
np_rng: np.random.Generator,
mode: str,
) -> Tuple[np.ndarray, np.ndarray, List[Dict[str, Any]]]:
"""Return ``(left, right, cell_records)``. One record per cell with
``row``, ``col``, ``perturbed`` (bool), ``cx``, ``cy``, ``radius``."""
n_channels = 3 if mode == "rgb" else 1
channels_left = [
generate_field(np_rng, shape=(PANEL_H, PANEL_W)) for _ in range(n_channels)
]
channels_right = [c.copy() for c in channels_left]
perturbed = set(_sample_perturbed_cells(rng))
cell_records: List[Dict[str, Any]] = []
for row in range(GRID_N):
for col in range(GRID_N):
cx, cy = _cell_center(row, col)
is_perturbed = (row, col) in perturbed
if is_perturbed:
for ch_left, ch_right in zip(channels_left, channels_right):
ch_std = float(np.std(ch_left)) or 1.0
_apply_radial_perturbation(
np_rng, ch_left, ch_right, cx, cy, CIRCLE_RADIUS, ch_std,
)
cell_records.append({
"row": row,
"col": col,
"perturbed": is_perturbed,
"cx": int(cx),
"cy": int(cy),
"radius": int(CIRCLE_RADIUS),
})
if mode == "rgb":
left = np.stack(channels_left, axis=-1)
right = np.stack(channels_right, axis=-1)
else:
left = channels_left[0]
right = channels_right[0]
return left, right, cell_records
# ---------------------------------------------------------------------------
# Rendering
# ---------------------------------------------------------------------------
LEGEND_SCALE = 0.4 # legend is 40% the dimensions of a field panel
def _legend_dims() -> Tuple[int, int]:
return int(round(PANEL_W * LEGEND_SCALE)), int(round(PANEL_H * LEGEND_SCALE))
def _panel_origins() -> Tuple[Tuple[float, float],
Tuple[float, float],
Tuple[float, float]]:
"""(ox, oy) for legend (small, vertically centered), left field, right
field. Layout: [legend] [GAP] [Field A] [GAP] [Field B]."""
oy_field = MARGIN_PX + LABEL_HEIGHT
leg_w, leg_h = _legend_dims()
ox_legend = MARGIN_PX
oy_legend = oy_field + (PANEL_H - leg_h) / 2
ox_left = ox_legend + leg_w + GAP_PX
ox_right = ox_left + PANEL_W + GAP_PX
return (ox_legend, oy_legend), (ox_left, oy_field), (ox_right, oy_field)
def _canvas_size() -> Tuple[int, int]:
leg_w, _ = _legend_dims()
w = MARGIN_PX + leg_w + GAP_PX + PANEL_W + GAP_PX + PANEL_W + MARGIN_PX
h = MARGIN_PX + LABEL_HEIGHT + PANEL_H + MARGIN_PX
return int(w), int(h)
def _draw_legend(ax: plt.Axes, ox: float, oy: float) -> None:
"""Small index-key panel: light grey background, N×N gridlines, each
cell labeled with its 1-based row-major number in bold font."""
leg_w, leg_h = _legend_dims()
cell_w = leg_w / GRID_N
cell_h = leg_h / GRID_N
legend_bg = mpatches.Rectangle(
(ox, oy), leg_w, leg_h,
facecolor="#e8e6e0", edgecolor=BORDER_COLOR,
linewidth=BORDER_WIDTH, zorder=2,
)
ax.add_patch(legend_bg)
for i in range(1, GRID_N):
gx = ox + i * cell_w
ax.plot([gx, gx], [oy, oy + leg_h],
color="#888", linewidth=GRID_LINE_WIDTH, zorder=3)
gy = oy + i * cell_h
ax.plot([ox, ox + leg_w], [gy, gy],
color="#888", linewidth=GRID_LINE_WIDTH, zorder=3)
fontsize = max(10, int(min(cell_w, cell_h) * 0.36))
for r in range(GRID_N):
for c in range(GRID_N):
n = r * GRID_N + c + 1
cx = ox + c * cell_w + cell_w / 2
cy = oy + r * cell_h + cell_h / 2
ax.text(cx, cy, str(n),
ha="center", va="center",
fontsize=fontsize, fontweight="bold",
color="#222", zorder=4)
def _normalise(field: np.ndarray, v_lo: float, v_hi: float) -> np.ndarray:
if v_hi <= v_lo:
return np.zeros_like(field, dtype=np.float64)
return (field - v_lo) / (v_hi - v_lo)
def _field_to_rgba(
field: np.ndarray,
mode: str,
v_lo: Any,
v_hi: Any,
np_rng: np.random.Generator,
) -> np.ndarray:
if mode == "rgb":
norm = np.stack(
[_normalise(field[..., c], v_lo[c], v_hi[c]) for c in range(3)],
axis=-1,
)
norm = norm + np_rng.uniform(-JITTER_AMPLITUDE, JITTER_AMPLITUDE, size=norm.shape)
norm = np.clip(norm, 0.0, 1.0)
alpha = np.ones(norm.shape[:2] + (1,), dtype=norm.dtype)
rgba = np.concatenate([norm, alpha], axis=-1)
else:
norm = _normalise(field, v_lo, v_hi)
norm = norm + np_rng.uniform(-JITTER_AMPLITUDE, JITTER_AMPLITUDE, size=norm.shape)
norm = np.clip(norm, 0.0, 1.0)
rgba = plt.get_cmap(mode)(norm)
return (rgba * 255.0 + 0.5).astype(np.uint8)
def _draw_grid(ax: plt.Axes, ox: float, oy: float) -> None:
"""Draw the 3×3 white gridlines on a panel (2 vertical + 2 horizontal)."""
for i in range(1, GRID_N):
gx = ox + i * CELL_W
ax.plot(
[gx, gx], [oy, oy + PANEL_H],
color=GRID_LINE_COLOR, linewidth=GRID_LINE_WIDTH,
alpha=GRID_LINE_ALPHA, zorder=4,
)
gy = oy + i * CELL_H
ax.plot(
[ox, ox + PANEL_W], [gy, gy],
color=GRID_LINE_COLOR, linewidth=GRID_LINE_WIDTH,
alpha=GRID_LINE_ALPHA, zorder=4,
)
def _render(
out_path: Path,
left: np.ndarray,
right: np.ndarray,
mode: str,
np_rng: np.random.Generator,
cell_records: List[Dict[str, Any]] | None = None,
) -> None:
w, h = _canvas_size()
dpi = 100
fig, ax = plt.subplots(1, 1, figsize=(w / dpi, h / dpi), dpi=dpi)
ax.set_xlim(0, w)
ax.set_ylim(h, 0)
ax.set_aspect("auto")
ax.axis("off")
fig.patch.set_facecolor(BG_COLOR)
ax.set_facecolor(BG_COLOR)
(ox_legend, oy_legend), (ox_left, oy), (ox_right, _) = _panel_origins()
_draw_legend(ax, ox_legend, oy_legend)
leg_w, _ = _legend_dims()
ax.text(
ox_legend + leg_w / 2, oy_legend - 12,
"Index", ha="center", va="bottom",
fontsize=13, fontweight="bold", color=LABEL_COLOR,
)
if mode == "rgb":
v_lo, v_hi = [], []
for c in range(3):
both = np.concatenate([left[..., c].ravel(), right[..., c].ravel()])
v_lo.append(float(np.quantile(both, 0.01)))
v_hi.append(float(np.quantile(both, 0.99)))
else:
both = np.concatenate([left.ravel(), right.ravel()])
v_lo = float(np.quantile(both, 0.01))
v_hi = float(np.quantile(both, 0.99))
left_rgba = _field_to_rgba(left, mode, v_lo, v_hi, np_rng)
right_rgba = _field_to_rgba(right, mode, v_lo, v_hi, np_rng)
ax.imshow(
left_rgba,
extent=(ox_left, ox_left + PANEL_W, oy + PANEL_H, oy),
interpolation="nearest",
zorder=2,
)
ax.imshow(
right_rgba,
extent=(ox_right, ox_right + PANEL_W, oy + PANEL_H, oy),
interpolation="nearest",
zorder=2,
)
for ox in (ox_left, ox_right):
border = mpatches.Rectangle(
(ox, oy), PANEL_W, PANEL_H,
facecolor="none", edgecolor=BORDER_COLOR,
linewidth=BORDER_WIDTH, zorder=3,
)
ax.add_patch(border)
_draw_grid(ax, ox, oy)
ax.text(
ox_left + PANEL_W / 2, MARGIN_PX + LABEL_HEIGHT * 0.5,
"Field A", ha="center", va="center",
fontsize=15, fontweight="bold", color=LABEL_COLOR,
)
ax.text(
ox_right + PANEL_W / 2, MARGIN_PX + LABEL_HEIGHT * 0.5,
"Field B", ha="center", va="center",
fontsize=15, fontweight="bold", color=LABEL_COLOR,
)
if cell_records:
for rec in cell_records:
if not rec["perturbed"]:
continue
cx, cy, rr = rec["cx"], rec["cy"], rec["radius"]
for ox in (ox_left, ox_right):
ax.add_patch(mpatches.Circle(
(ox + cx, oy + cy), rr,
facecolor="none", edgecolor=HIGHLIGHT_COLOR,
linewidth=2.2, zorder=5,
))
fig.savefig(out_path, facecolor=BG_COLOR)
plt.close(fig)
def render_pair(
out_path: Path,
left: np.ndarray,
right: np.ndarray,
mode: str,
np_rng: np.random.Generator,
) -> None:
_render(out_path, left, right, mode, np_rng)
def render_answer(
out_path: Path,
left: np.ndarray,
right: np.ndarray,
cell_records: List[Dict[str, Any]],
mode: str,
np_rng: np.random.Generator,
) -> None:
_render(out_path, left, right, mode, np_rng, cell_records)
# ---------------------------------------------------------------------------
# Annotation
# ---------------------------------------------------------------------------
def build_annotation(
image_name: str,
cell_records: List[Dict[str, Any]],
mode: str,
) -> Dict[str, Any]:
num_identical = sum(1 for r in cell_records if not r["perturbed"])
num_different = GRID_N * GRID_N - num_identical
diff_indices = sorted(
r["row"] * GRID_N + r["col"] + 1
for r in cell_records if r["perturbed"]
)
answer = ", ".join(str(i) for i in diff_indices) if diff_indices else "none"
return {
"image": image_name,
"color_mode": mode,
"grid": GRID_N,
"num_cells": GRID_N * GRID_N,
"num_identical": num_identical,
"num_different": num_different,
"diff_indices": diff_indices,
"cells": cell_records,
"question": _build_question(),
"answer": answer,
}
# ---------------------------------------------------------------------------
# Dataset generation
# ---------------------------------------------------------------------------
def generate_dataset(
rng: random.Random,
np_rng: np.random.Generator,
count: int,
output_dir: Path,
) -> None:
images_dir = output_dir / "images"
answers_dir = output_dir / "answers"
images_dir.mkdir(parents=True, exist_ok=True)
answers_dir.mkdir(parents=True, exist_ok=True)
annotations: List[Dict[str, Any]] = []
data_items: List[Dict[str, Any]] = []
for idx in tqdm(range(count), desc="Generating field diff pairs"):
mode = rng.choice(COLOR_MODES)
for _ in range(20):
try:
left, right, cell_records = build_sample(rng, np_rng, mode)
break
except RuntimeError:
continue
else:
raise RuntimeError(f"Failed to build sample {idx}")
image_name = f"field_diff_{idx:05d}.png"
img_path = images_dir / image_name
ans_path = answers_dir / image_name
render_pair(img_path, left, right, mode, np_rng)
render_answer(ans_path, left, right, cell_records, mode, np_rng)
rel_image = f"images/{image_name}"
diff_indices = sorted(
r["row"] * GRID_N + r["col"] + 1
for r in cell_records if r["perturbed"]
)
answer = ", ".join(str(i) for i in diff_indices) if diff_indices else "none"
annotations.append(build_annotation(rel_image, cell_records, mode))
data_items.append({
"image": rel_image,
"question": _build_question(),
"answer": answer,
})
with (output_dir / "annotations.jsonl").open("w", encoding="utf-8") as fh:
for rec in annotations:
fh.write(json.dumps(rec) + "\n")
data_json = {
"task": "spot_the_field_diff",
"category": "visual_attribute_transfer",
"count": len(data_items),
"items": data_items,
}
with (output_dir / "data.json").open("w", encoding="utf-8") as fh:
json.dump(data_json, fh, indent=2)
fh.write("\n")
# ---------------------------------------------------------------------------
# CLI
# ---------------------------------------------------------------------------
def parse_args() -> argparse.Namespace:
p = argparse.ArgumentParser(
description="Generate 'Spot the Field Diff' visual benchmark dataset."
)
p.add_argument("--output-root", type=Path, default=".")
p.add_argument("--count", type=int, default=20)
p.add_argument("--seed", type=int, default=42)
p.add_argument("--difficulty", type=int, default=5,
help="Integer difficulty >=0; scales perturbed cells and blend subtlety.")
return p.parse_args()
def main() -> None:
args = parse_args()
rng = random.Random(args.seed)
np_rng = np.random.default_rng(args.seed)
d = max(0, int(args.difficulty))
global GRID_N, PANEL_W, PANEL_H, MIN_PERTURBED, MAX_PERTURBED
global MIN_BLEND_DIFF_MULT, MIN_BLEND_MEAN_DIFF_MULT, FIELD_FREQUENCY_SCALE
GRID_N = 3 + d // 3
PANEL_W = CELL_W * GRID_N
PANEL_H = CELL_H * GRID_N
MIN_PERTURBED = 1
MAX_PERTURBED = GRID_N * GRID_N
MIN_BLEND_DIFF_MULT = 3.0 - 0.1 * d
MIN_BLEND_MEAN_DIFF_MULT = max(0.5, 1.0 - 0.05 * d)
FIELD_FREQUENCY_SCALE = max(0.4, 1.0 - 0.08 * d)
generate_dataset(rng, np_rng, args.count, args.output_root)
print(f"Saved {args.count} field diff pairs to {args.output_root}")
if __name__ == "__main__":
main()
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