Working Python version for Commodore.

c64view/dither.py

@@ -0,0 +1,136 @@
+"""Palette-constrained dithering.
+
+Every routine takes the working image in CIELAB plus a per-pixel table of the
+palette indices that pixel is *allowed* to use (because the VIC-II only lets a
+given screen cell show a small set of colours), and returns an (H,W) image of
+chosen palette indices (0..15).  Because the allowed set is per-pixel, error that
+diffuses across a cell boundary is automatically re-clamped to the neighbour
+cell's own colours -- exactly the constraint real C64 hardware imposes.
+"""
+
+from __future__ import annotations
+
+import numpy as np
+
+DITHER_MODES = ["bayer", "floyd", "atkinson", "stucki", "jarvis", "none"]
+
+
+def bayer_matrix(n: int) -> np.ndarray:
+    """Normalised (0..1) Bayer threshold matrix of size n x n (n power of two)."""
+    if n == 1:
+        return np.array([[0.0]])
+    smaller = bayer_matrix(n // 2)
+    m = np.block([
+        [4 * smaller + 0, 4 * smaller + 2],
+        [4 * smaller + 3, 4 * smaller + 1],
+    ])
+    return m / (n * n)
+
+
+def _gather_colors(palette_lab: np.ndarray, allowed: np.ndarray) -> np.ndarray:
+    # allowed: (H,W,K) palette indices -> (H,W,K,3) Lab
+    return palette_lab[allowed]
+
+
+def quantize_ordered(img_lab, allowed, palette_lab, strength=1.0, n=8):
+    """Ordered (Bayer) dithering between the two best colours of each pixel's set.
+
+    For every pixel we find its nearest and second-nearest allowed colour, project
+    the pixel onto the segment between them, and use the Bayer threshold to decide
+    which of the two to emit -- giving smooth ordered blends without ever leaving
+    the cell's legal colour set.
+    """
+    H, W, _ = img_lab.shape
+    colors = _gather_colors(palette_lab, allowed)            # (H,W,K,3)
+    d = np.sum((img_lab[:, :, None, :] - colors) ** 2, axis=-1)  # (H,W,K)
+
+    i1 = np.argmin(d, axis=-1)
+    d2 = np.array(d)
+    np.put_along_axis(d2, i1[..., None], np.inf, axis=-1)
+    i2 = np.argmin(d2, axis=-1)
+
+    yy, xx = np.indices((H, W))
+    c1 = colors[yy, xx, i1]                                  # (H,W,3)
+    c2 = colors[yy, xx, i2]
+    seg = c2 - c1
+    seg_len2 = np.sum(seg * seg, axis=-1) + 1e-9
+    t = np.sum((img_lab - c1) * seg, axis=-1) / seg_len2     # projection 0..1
+    t = np.clip(t * strength, 0.0, 1.0)
+
+    thr = bayer_matrix(n)
+    thr_full = thr[yy % n, xx % n]
+    pick2 = t > thr_full
+    chosen = np.where(pick2, i2, i1)
+    return np.take_along_axis(allowed, chosen[..., None], axis=-1)[..., 0]
+
+
+def _quantize_diffusion(img_lab, allowed, palette_lab, kernel, divisor):
+    """Generic serpentine error-diffusion constrained to per-pixel allowed sets."""
+    H, W, _ = img_lab.shape
+    work = img_lab.astype(np.float64).copy()
+    out = np.zeros((H, W), dtype=np.int64)
+    pal = palette_lab
+    for y in range(H):
+        cols = range(W) if (y % 2 == 0) else range(W - 1, -1, -1)
+        flip = 1 if (y % 2 == 0) else -1
+        for x in cols:
+            allow = allowed[y, x]
+            cand = pal[allow]
+            diff = cand - work[y, x]
+            k = int(allow[np.argmin(np.sum(diff * diff, axis=-1))])
+            out[y, x] = k
+            err = work[y, x] - pal[k]
+            for dx, dy, w in kernel:
+                nx, ny = x + dx * flip, y + dy
+                if 0 <= nx < W and 0 <= ny < H:
+                    work[ny, nx] += err * (w / divisor)
+    return out
+
+
+# (dx, dy, weight) relative to current pixel, assuming left-to-right scan.
+_FLOYD = [(1, 0, 7), (-1, 1, 3), (0, 1, 5), (1, 1, 1)]
+_ATKINSON = [(1, 0, 1), (2, 0, 1), (-1, 1, 1), (0, 1, 1), (1, 1, 1), (0, 2, 1)]
+# Larger kernels spread error further -> smoother gradients (best for grayscale).
+_STUCKI = [(1, 0, 8), (2, 0, 4),
+           (-2, 1, 2), (-1, 1, 4), (0, 1, 8), (1, 1, 4), (2, 1, 2),
+           (-2, 2, 1), (-1, 2, 2), (0, 2, 4), (1, 2, 2), (2, 2, 1)]
+_JARVIS = [(1, 0, 7), (2, 0, 5),
+           (-2, 1, 3), (-1, 1, 5), (0, 1, 7), (1, 1, 5), (2, 1, 3),
+           (-2, 2, 1), (-1, 2, 3), (0, 2, 5), (1, 2, 3), (2, 2, 1)]
+
+
+def quantize_floyd(img_lab, allowed, palette_lab):
+    return _quantize_diffusion(img_lab, allowed, palette_lab, _FLOYD, 16)
+
+
+def quantize_atkinson(img_lab, allowed, palette_lab):
+    return _quantize_diffusion(img_lab, allowed, palette_lab, _ATKINSON, 8)
+
+
+def quantize_stucki(img_lab, allowed, palette_lab):
+    return _quantize_diffusion(img_lab, allowed, palette_lab, _STUCKI, 42)
+
+
+def quantize_jarvis(img_lab, allowed, palette_lab):
+    return _quantize_diffusion(img_lab, allowed, palette_lab, _JARVIS, 48)
+
+
+def quantize_none(img_lab, allowed, palette_lab):
+    colors = _gather_colors(palette_lab, allowed)
+    d = np.sum((img_lab[:, :, None, :] - colors) ** 2, axis=-1)
+    i1 = np.argmin(d, axis=-1)
+    return np.take_along_axis(allowed, i1[..., None], axis=-1)[..., 0]
+
+
+def quantize(img_lab, allowed, palette_lab, mode="bayer"):
+    if mode == "bayer":
+        return quantize_ordered(img_lab, allowed, palette_lab)
+    if mode == "floyd":
+        return quantize_floyd(img_lab, allowed, palette_lab)
+    if mode == "atkinson":
+        return quantize_atkinson(img_lab, allowed, palette_lab)
+    if mode == "stucki":
+        return quantize_stucki(img_lab, allowed, palette_lab)
+    if mode == "jarvis":
+        return quantize_jarvis(img_lab, allowed, palette_lab)
+    return quantize_none(img_lab, allowed, palette_lab)