feat(scenegraph): add JSON serialization and implement top-down object/edge rendering

- Add save_scene_graph() and load_scene_graph() for persisting scene graphs to JSON
- Implement object node overlay (colored by label) in render_topdown_scene_map
- Implement edge arrows (room → object) in render_topdown_scene_map
- Add TopDownRenderStyle fields for object/edge visual configuration
- Add scene graph caching to verification notebook to skip rebuilds
- Add render_scene_graph_birdseye cell for full scene graph visualization
- Add display_objects_by_room and display_room_summary cells

mini-nav/simulator/topdown.py

@@ -16,6 +16,23 @@ class TopDownSceneElements:
     edges: Sequence[tuple[str, str]] = field(default_factory=tuple)
 
 
+# Default color palette for object labels (cycled if more labels than colors).
+_DEFAULT_LABEL_COLORS: dict[str, str] = {
+    "chair": "#e6194b",
+    "table": "#3cb44b",
+    "sofa": "#ffe119",
+    "cabinet": "#4363d8",
+    "shelf": "#f58231",
+    "lamp": "#911eb4",
+    "picture": "#42d4f4",
+    "window": "#f032e6",
+    "door": "#bfef45",
+    "plant": "#fabed4",
+}
+
+_FALLBACK_COLOR = "#808080"
+
+
 @dataclass(frozen=True)
 class TopDownRenderStyle:
     room_color: str = "red"
@@ -25,6 +42,18 @@ class TopDownRenderStyle:
     figure_size: tuple[int, int] = (8, 8)
     map_cmap: str = "gray"
     title: str = "RoomNode Top-Down Map"
+    # Object node style.
+    object_marker_size: int = 25
+    object_label_colors: dict[str, str] = field(
+        default_factory=lambda: dict(_DEFAULT_LABEL_COLORS)
+    )
+    object_fallback_color: str = _FALLBACK_COLOR
+    object_show_label: bool = True
+    object_label_fontsize: int = 6
+    # Edge style.
+    edge_color: str = "cyan"
+    edge_alpha: float = 0.4
+    edge_arrow_size: float = 8.0
 
 
 def render_topdown_scene_map(
@@ -35,13 +64,14 @@ def render_topdown_scene_map(
 ) -> Image.Image:
     """Render a top-down scene map as a PIL Image.
 
-    Uses matplotlib Agg backend (non-interactive) to draw room markers and
-    labels on the habitat top-down occupancy map, then returns the result
-    as a PIL Image.
+    Uses matplotlib Agg backend (non-interactive) to draw room markers,
+    object markers (colored by label), and edges (arrows from room to
+    object) on the habitat top-down occupancy map, then returns the
+    result as a PIL Image.
 
     Args:
         pathfinder: Habitat pathfinder instance.
-        elements: Scene elements containing room nodes to annotate.
+        elements: Scene elements containing room/object nodes and edges.
         meters_per_pixel: Resolution for the top-down map.
         style: Visual style configuration.
 
@@ -50,7 +80,6 @@ def render_topdown_scene_map(
 
     Raises:
         ValueError: If room_nodes is empty or meters_per_pixel <= 0.
-        NotImplementedError: If object_nodes or edges are provided.
     """
     if not elements.room_nodes:
         raise ValueError("room_nodes must not be empty")
@@ -58,12 +87,6 @@ def render_topdown_scene_map(
     if meters_per_pixel <= 0:
         raise ValueError("meters_per_pixel must be greater than 0")
 
-    if elements.object_nodes:
-        raise NotImplementedError("object_nodes overlay is not implemented yet")
-
-    if elements.edges:
-        raise NotImplementedError("edge overlay is not implemented yet")
-
     if style is None:
         style = TopDownRenderStyle()
 
@@ -84,7 +107,8 @@ def render_topdown_scene_map(
     ax = fig.add_subplot(111)
     ax.imshow(top_down_map, cmap=style.map_cmap)
 
-    # Annotate room positions and labels.
+    # --- Room nodes ---
+    room_grid_positions: dict[str, tuple[int, int]] = {}
     for room_node in elements.room_nodes:
         grid_y, grid_x = maps.to_grid(
             float(room_node.center[2]),
@@ -92,6 +116,7 @@ def render_topdown_scene_map(
             top_down_map.shape,
             pathfinder=pathfinder,
         )
+        room_grid_positions[room_node.room_id] = (grid_x, grid_y)
         ax.scatter(grid_x, grid_y, c=style.room_color, s=style.room_marker_size)
         ax.text(
             grid_x + style.room_label_offset,
@@ -101,6 +126,74 @@ def render_topdown_scene_map(
             fontsize=8,
         )
 
+    # --- Object nodes (colored by label) ---
+    obj_grid_positions: dict[str, tuple[int, int]] = {}
+    drawn_labels: set[str] = set()
+
+    for obj_node in elements.object_nodes:
+        if obj_node.position is None:
+            continue
+        grid_y, grid_x = maps.to_grid(
+            float(obj_node.position[2]),
+            float(obj_node.position[0]),
+            top_down_map.shape,
+            pathfinder=pathfinder,
+        )
+        obj_grid_positions[obj_node.obj_id] = (grid_x, grid_y)
+
+        label = obj_node.label or "unknown"
+        color = style.object_label_colors.get(label, style.object_fallback_color)
+
+        # Only add to legend once per label.
+        legend_label = label if label not in drawn_labels else None
+        drawn_labels.add(label)
+
+        ax.scatter(
+            grid_x,
+            grid_y,
+            c=color,
+            s=style.object_marker_size,
+            marker="^",
+            label=legend_label,
+            zorder=3,
+        )
+
+        if style.object_show_label:
+            ax.text(
+                grid_x + 1,
+                grid_y + 1,
+                label,
+                color=color,
+                fontsize=style.object_label_fontsize,
+            )
+
+    # --- Edges (arrows from room → object) ---
+    for room_id, obj_id in elements.edges:
+        room_pos = room_grid_positions.get(room_id)
+        obj_pos = obj_grid_positions.get(obj_id)
+        if room_pos is None or obj_pos is None:
+            continue
+        ax.annotate(
+            "",
+            xy=obj_pos,
+            xytext=room_pos,
+            arrowprops=dict(
+                arrowstyle="->",
+                color=style.edge_color,
+                alpha=style.edge_alpha,
+                lw=0.8,
+            ),
+        )
+
+    # --- Legend (only if object labels were drawn) ---
+    if drawn_labels:
+        ax.legend(
+            loc="upper right",
+            fontsize=7,
+            markerscale=0.8,
+            framealpha=0.7,
+        )
+
     ax.set_title(style.title)
     ax.axis("off")
     fig.canvas.draw()