fix(ocr-pipeline): improve page crop spine detection and cell assignment

1. page_crop: Score all dark runs by center-proximity × darkness ×
   narrowness instead of picking the widest. Fixes ad810209 where a
   wide dark area at 35% was chosen over the actual spine at 50%.

2. cv_words_first: Replace x-center-only word→column assignment with
   overlap-based three-pass strategy (overlap → midpoint-range → nearest).
   Fixes truncated German translations like "Schal" instead of
   "Schal - die Schals" in session 079cd0d9.

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

klausur-service/backend/cv_words_first.py

@@ -124,13 +124,43 @@ def _cluster_rows(
 # ---------------------------------------------------------------------------
 
 def _assign_word_to_column(word: Dict, columns: List[Dict]) -> int:
-    """Return column index for a word based on its X-center."""
-    x_center = word['left'] + word['width'] / 2
+    """Return column index for a word based on overlap, then center, then nearest.
+
+    Three-pass strategy (consistent with _assign_row_words_to_columns):
+    1. Overlap-based: assign to column with maximum horizontal overlap.
+    2. Midpoint-range: if no overlap, use midpoints between adjacent columns.
+    3. Nearest center: last resort fallback.
+    """
+    w_left = word['left']
+    w_right = w_left + word['width']
+    w_center = w_left + word['width'] / 2
+
+    # Pass 1: overlap-based
+    best_col = -1
+    best_overlap = 0
     for col in columns:
-        if col['x_min'] <= x_center < col['x_max']:
+        overlap = max(0, min(w_right, col['x_max']) - max(w_left, col['x_min']))
+        if overlap > best_overlap:
+            best_overlap = overlap
+            best_col = col['index']
+    if best_col >= 0 and best_overlap > 0:
+        return best_col
+
+    # Pass 2: midpoint-range (non-overlapping assignment zones)
+    for ci, col in enumerate(columns):
+        if ci == 0:
+            assign_left = 0
+        else:
+            assign_left = (columns[ci - 1]['x_max'] + col['x_min']) / 2
+        if ci == len(columns) - 1:
+            assign_right = float('inf')
+        else:
+            assign_right = (col['x_max'] + columns[ci + 1]['x_min']) / 2
+        if assign_left <= w_center < assign_right:
             return col['index']
-    # Fallback: nearest column
-    return min(columns, key=lambda c: abs((c['x_min'] + c['x_max']) / 2 - x_center))['index']
+
+    # Pass 3: nearest column center
+    return min(columns, key=lambda c: abs((c['x_min'] + c['x_max']) / 2 - w_center))['index']
 
 
 def _assign_word_to_row(word: Dict, rows: List[Dict]) -> int:

klausur-service/backend/page_crop.py

@@ -83,10 +83,9 @@ def detect_page_splits(
                       darkest_val, spine_thresh)
         return []
 
-    # Find the contiguous dark region (spine area)
+    # Find ALL contiguous dark runs in the center region
     is_dark = center_brightness < spine_thresh
-    # Find the widest dark run
-    best_start, best_end = 0, 0
+    dark_runs: list = []  # list of (start, end) pairs
     run_start = -1
     for i in range(len(is_dark)):
         if is_dark[i]:
@@ -94,20 +93,70 @@ def detect_page_splits(
                 run_start = i
         else:
             if run_start >= 0:
-                if i - run_start > best_end - best_start:
-                    best_start, best_end = run_start, i
+                dark_runs.append((run_start, i))
                 run_start = -1
-    if run_start >= 0 and len(is_dark) - run_start > best_end - best_start:
-        best_start, best_end = run_start, len(is_dark)
+    if run_start >= 0:
+        dark_runs.append((run_start, len(is_dark)))
 
-    spine_w = best_end - best_start
-    if spine_w < w * 0.01:
-        logger.debug("Spine too narrow: %dpx (< %dpx)", spine_w, int(w * 0.01))
+    # Filter out runs that are too narrow (< 1% of image width)
+    min_spine_px = int(w * 0.01)
+    dark_runs = [(s, e) for s, e in dark_runs if e - s >= min_spine_px]
+
+    if not dark_runs:
+        logger.debug("No dark runs wider than %dpx in center region", min_spine_px)
         return []
 
+    # Score each dark run: prefer centered, dark, narrow valleys
+    center_region_len = center_hi - center_lo
+    image_center_in_region = (w * 0.5 - center_lo)  # x=50% mapped into region coords
+    best_score = -1.0
+    best_start, best_end = dark_runs[0]
+
+    for rs, re in dark_runs:
+        run_width = re - rs
+        run_center = (rs + re) / 2.0
+
+        # --- Factor 1: Proximity to image center (gaussian, sigma = 15% of region) ---
+        sigma = center_region_len * 0.15
+        dist = abs(run_center - image_center_in_region)
+        center_factor = float(np.exp(-0.5 * (dist / sigma) ** 2))
+
+        # --- Factor 2: Darkness (how dark is the valley relative to threshold) ---
+        run_brightness = float(np.mean(center_brightness[rs:re]))
+        # Normalize: 1.0 when run_brightness == 0, 0.0 when run_brightness == spine_thresh
+        darkness_factor = max(0.0, (spine_thresh - run_brightness) / spine_thresh)
+
+        # --- Factor 3: Narrowness bonus (spine shadows are narrow, not wide plateaus) ---
+        # Typical spine: 1-5% of image width. Penalise runs wider than ~8%.
+        width_frac = run_width / w
+        if width_frac <= 0.05:
+            narrowness_bonus = 1.0
+        elif width_frac <= 0.15:
+            narrowness_bonus = 1.0 - (width_frac - 0.05) / 0.10  # linear decay 1.0 → 0.0
+        else:
+            narrowness_bonus = 0.0
+
+        score = center_factor * darkness_factor * (0.3 + 0.7 * narrowness_bonus)
+
+        logger.debug(
+            "Dark run x=%d..%d (w=%d): center_f=%.3f dark_f=%.3f narrow_b=%.3f → score=%.4f",
+            center_lo + rs, center_lo + re, run_width,
+            center_factor, darkness_factor, narrowness_bonus, score,
+        )
+
+        if score > best_score:
+            best_score = score
+            best_start, best_end = rs, re
+
+    spine_w = best_end - best_start
     spine_x = center_lo + best_start
     spine_center = spine_x + spine_w // 2
 
+    logger.debug(
+        "Best spine candidate: x=%d..%d (w=%d), score=%.4f",
+        spine_x, spine_x + spine_w, spine_w, best_score,
+    )
+
     # Verify: must have bright (paper) content on BOTH sides
     left_brightness = float(np.mean(brightness_smooth[max(0, spine_x - w // 10):spine_x]))
     right_end = center_lo + best_end

klausur-service/backend/tests/test_page_crop.py

@@ -15,6 +15,7 @@ import pytest
 
 from page_crop import (
     detect_and_crop_page,
+    detect_page_splits,
     _detect_format,
     _detect_edge_projection,
     _detect_left_edge_shadow,
@@ -465,3 +466,101 @@ class TestCropDeterminism:
             assert np.array_equal(ref_crop, crop), (
                 f"Run {i} produced different pixel output"
             )
+
+
+# ---------------------------------------------------------------------------
+# Tests: detect_page_splits — spine scoring logic
+# ---------------------------------------------------------------------------
+
+def _make_book_spread(h: int = 1616, w: int = 2288) -> np.ndarray:
+    """Create a synthetic landscape book spread (two pages side by side).
+
+    Simulates the ad810209 failure case:
+    - A narrow spine shadow near the center (~50% of width)
+    - A wider dark area off-center (~35% of width), simulating a text column
+    - Bright paper flanking the spine on both sides
+    """
+    img = np.full((h, w, 3), 230, dtype=np.uint8)
+
+    # --- Spine shadow: narrow dark valley centered at x = w/2 (1144) ---
+    spine_center = w // 2
+    spine_half_w = 30  # ~60px wide total
+    for x in range(spine_center - spine_half_w, spine_center + spine_half_w + 1):
+        dist = abs(x - spine_center)
+        # Brightness dips from 230 (paper) to 130 (spine)
+        brightness = int(130 + (230 - 130) * min(dist / spine_half_w, 1.0))
+        img[:, x] = brightness
+
+    # --- Off-center dark area at ~35% of width (x=799), wider than spine ---
+    dark_center = int(w * 0.35)
+    dark_half_w = 80  # ~160px wide total (wider than spine)
+    for x in range(dark_center - dark_half_w, dark_center + dark_half_w + 1):
+        dist = abs(x - dark_center)
+        # Brightness dips from 230 to 140 (slightly less dark than spine)
+        brightness = int(140 + (230 - 140) * min(dist / dark_half_w, 1.0))
+        img[:, x] = min(img[0, x, 0], brightness)  # don't overwrite spine if overlapping
+
+    return img
+
+
+class TestDetectPageSplits:
+    def test_portrait_image_returns_empty(self):
+        """Portrait images (width < height * 1.15) should not be split."""
+        img = np.full((1000, 800, 3), 200, dtype=np.uint8)
+        assert detect_page_splits(img) == []
+
+    def test_uniform_image_returns_empty(self):
+        """Uniform brightness image should not detect any spine."""
+        img = np.full((800, 1600, 3), 220, dtype=np.uint8)
+        assert detect_page_splits(img) == []
+
+    def test_prefers_centered_spine_over_wider_offcenter_dark(self):
+        """Scoring should pick the centered narrow spine over a wider off-center dark area.
+
+        This is the regression test for session ad810209 where the old algorithm
+        picked x=799 (35%) instead of x=1144 (50%).
+        """
+        img = _make_book_spread(h=1616, w=2288)
+        pages = detect_page_splits(img)
+
+        assert len(pages) == 2, f"Expected 2 pages, got {len(pages)}"
+
+        # Split point should be near the center (x ~ 1144), not at ~799
+        split_x = pages[0]["width"]  # pages[0] width = split point
+        center = 2288 / 2  # 1144
+
+        assert abs(split_x - center) < 100, (
+            f"Split at x={split_x}, expected near center {center:.0f}. "
+            f"Old bug would have split at ~799."
+        )
+
+    def test_split_produces_two_reasonable_pages(self):
+        """Both pages should be at least 15% of total width."""
+        img = _make_book_spread()
+        pages = detect_page_splits(img)
+
+        if len(pages) == 2:
+            w = img.shape[1]
+            for p in pages:
+                assert p["width"] >= w * 0.15, (
+                    f"Page {p['page_index']} too narrow: {p['width']}px "
+                    f"(< {w * 0.15:.0f}px)"
+                )
+
+    def test_page_indices_sequential(self):
+        """Page indices should be 0, 1, ..."""
+        img = _make_book_spread()
+        pages = detect_page_splits(img)
+        if pages:
+            indices = [p["page_index"] for p in pages]
+            assert indices == list(range(len(pages)))
+
+    def test_pages_cover_full_width(self):
+        """Pages should cover the full image width without gaps or overlaps."""
+        img = _make_book_spread()
+        pages = detect_page_splits(img)
+        if len(pages) >= 2:
+            w = img.shape[1]
+            assert pages[0]["x"] == 0
+            total_w = sum(p["width"] for p in pages)
+            assert total_w == w, f"Total page width {total_w} != image width {w}"