Fix startup crash: replace sklearn k-means with pure numpy implementation

sklearn was not installed in the container, causing ModuleNotFoundError on
import of ai_tools.py and preventing the server from starting.

Replaced with a self-contained numpy k-means++ implementation:
- k-means++ seeding for better initial centers
- 20-iteration Lloyd's algorithm
- Same output: hex colors sorted by cluster frequency

No new dependencies required.

https://claude.ai/code/session_01B58MaJCU1R6KwBDJCp8AfN

backend/app/routers/ai_tools.py

@@ -511,8 +511,6 @@ async def enhance(req: EnhanceRequest):
 
 # ─── Extract colors ───────────────────────────────────────────────────────────
 
-from sklearn.cluster import KMeans as _KMeans
-
 class ExtractColorsRequest(BaseModel):
     image: str      # base64
     count: int = 6
@@ -520,28 +518,49 @@ class ExtractColorsRequest(BaseModel):
 
 def _extract_colors(image_bytes: bytes, count: int) -> list[str]:
     """
-    Resize image to 150×150, k-means cluster pixels into `count` groups,
-    sort by cluster size (largest first), return as hex strings.
+    Resize image to 150×150, k-means cluster pixels into `count` groups
+    using pure numpy (no sklearn dependency), return hex strings by frequency.
     """
+    import numpy as np
+    from PIL import Image
+    from io import BytesIO
+
     count = max(1, min(count, 32))
 
-    pil = _Image.open(_io.BytesIO(image_bytes)).convert("RGB").resize((150, 150))
-    pixels = _np.array(pil, dtype=_np.float32).reshape(-1, 3)  # (N, 3)
+    pil    = Image.open(BytesIO(image_bytes)).convert("RGB").resize((150, 150))
+    pixels = np.array(pil, dtype=np.float32).reshape(-1, 3)  # (22500, 3)
+    n      = len(pixels)
 
-    km = _KMeans(n_clusters=count, n_init=10, random_state=42)
-    labels = km.fit_predict(pixels)
-    centers = km.cluster_centers_  # (count, 3)
+    # Initialise centers with k-means++ seeding
+    rng     = np.random.default_rng(42)
+    centers = [pixels[rng.integers(n)]]
+    for _ in range(count - 1):
+        dists = np.min([np.sum((pixels - c) ** 2, axis=1) for c in centers], axis=0)
+        probs = dists / dists.sum()
+        centers.append(pixels[rng.choice(n, p=probs)])
+    centers = np.array(centers)
 
-    # Count pixels per cluster and sort by frequency descending
-    counts = _np.bincount(labels, minlength=count)
-    order = _np.argsort(-counts)  # descending
+    labels = np.zeros(n, dtype=np.int32)
+    for _ in range(20):                         # max 20 iterations
+        # Assign each pixel to nearest center
+        dists  = np.sum((pixels[:, None] - centers[None]) ** 2, axis=2)  # (n, k)
+        new_labels = np.argmin(dists, axis=1)
+        if np.all(new_labels == labels):
+            break
+        labels = new_labels
+        # Recompute centers
+        for k in range(count):
+            mask = labels == k
+            if mask.any():
+                centers[k] = pixels[mask].mean(axis=0)
 
-    hex_colors = []
-    for idx in order:
-        r, g, b = centers[idx].astype(int).clip(0, 255)
-        hex_colors.append(f"#{r:02x}{g:02x}{b:02x}")
+    counts = np.bincount(labels, minlength=count)
+    order  = np.argsort(-counts)
 
-    return hex_colors
+    return [
+        "#{:02x}{:02x}{:02x}".format(*centers[i].astype(int).clip(0, 255))
+        for i in order
+    ]
 
 
 @router.post("/extract-colors")