Omni3D — Gemma4-31B — sample 91

Task Analysis

The objective is to determine the direction of the TV relative to a person standing at a Christmas tree and facing the camera.

• Reference Point: The Christmas tree.
• Reference Orientation (North): The vector from the Christmas tree to the camera.
• Target Object: The TV.
• Coordinate System: Object-relative 3D space. North (N) is defined as the direction the person is facing (towards the camera). East (E) is the direction to the person's right while facing North.
• Answer Format: One of the cardinal or intercardinal directions: {N, NE, E, SE, S, SW, W, NW}.

Information Needs

To compute the direction quantitatively, I need:

1. The 3D world position of the camera.
2. The 3D world position of the Christmas tree.
3. The 3D world position of the TV.
4. A way to define the "Right" (East) vector relative to the person's orientation.

Computation Plan

1. Scene Reconstruction: Perform a 3D reconstruction of the single provided image to obtain depth maps and camera pose.
   • recon = tools.Reconstruct.Reconstruct(InputImages)
2. Object Segmentation:
   • Use tools.SAM3.segment_image_by_text to find masks for the "christmas tree" and "TV".
   • If text prompts fail or return multiple ambiguous objects, use vlm.locate to get bounding boxes for the specific Christmas tree and TV, then use tools.SAM3.segment_image_by_box.
3. Visual Verification:
   • Use show() to display the original image alongside the segmentation masks for the Christmas tree and TV to ensure they are correctly identified.
4. 3D Coordinate Extraction:
   • Extract the camera position: cam_pos = recon.extrinsics[0][:3, 3].
   • Extract the 3D centroid of the Christmas tree: tree_pos = seg_tree.get_centroid_3d(recon, frame=0, object=0).
   • Extract the 3D centroid of the TV: tv_pos = seg_tv.get_centroid_3d(recon, frame=0, object=0).
5. Direction Vector Calculation:
   • Define the North vector: $\vec{N} = \text{normalize}(\text{cam_pos} - \text{tree_pos})$.
   • Define the World Up vector: $\vec{Up} = [0, 1, 0]$.
   • Define the East vector (to the person's right): $\vec{E} = \text{normalize}(\vec{N} \times \vec{Up})$.
   • Define the vector to the TV: $\vec{V}_{tv} = \text{normalize}(\text{tv_pos} - \text{tree_pos})$.
6. Angular Projection:
   • Calculate the projection of $\vec{V}_{tv}$ onto the North and East axes:
     • $dot_N = \vec{V}_{tv} \cdot \vec{N}$
     • $dot_E = \vec{V}_{tv} \cdot \vec{E}$
   • Calculate the angle $\theta = \text{atan2}(dot_E, dot_N)$ in degrees.
7. Direction Mapping:
   • Map $\theta$ to the 8-point compass:
     • $-22.5^\circ$ to $22.5^\circ \rightarrow \text{N}$
     • $22.5^\circ$ to $67.5^\circ \rightarrow \text{NE}$
     • $67.5^\circ$ to $112.5^\circ \rightarrow \text{E}$
     • $112.5^\circ$ to $157.5^\circ \rightarrow \text{SE}$
     • $157.5^\circ$ to $202.5^\circ \rightarrow \text{S}$
     • $202.5^\circ$ to $247.5^\circ \rightarrow \text{SW}$
     • $247.5^\circ$ to $292.5^\circ \rightarrow \text{W}$
     • $292.5^\circ$ to $337.5^\circ \rightarrow \text{NW}$

Verification

• Mask Integrity: Visually confirm that the masks for the TV and Christmas tree are accurate and not empty.
• 3D Sanity Check: Print the 3D coordinates and ensure they are not NaN and are physically plausible (e.g., objects are on the floor).
• Cross-Validation: Use vlm.ask_with_thinking to ask for a qualitative description of the TV's position relative to the Christmas tree and the camera (e.g., "Is the TV to the left or right of the Christmas tree from the camera's perspective?") to verify the computed direction.
• Coordinate Logic: Double-check that the East vector is correctly derived as the right-hand side of the person facing the camera.

Fallbacks

• If the 3D reconstruction is too noisy for a single frame, I will rely more heavily on vlm.ask_with_thinking to establish the relative 2D layout and use the camera's optical axis as a proxy for the North vector.
• If the TV is not clearly visible, I will use vlm.locate to search for it in the image.

CHECKLIST

[
  {"priority": "HIGH", "description": "Verify that the masks for the Christmas tree and TV are correctly placed and non-empty"},
  {"priority": "HIGH", "description": "Confirm the North vector is correctly defined as the vector from the tree to the camera"},
  {"priority": "HIGH", "description": "Ensure the East vector is correctly calculated as the person's right-hand side"},
  {"priority": "MEDIUM", "description": "Cross-check the computed direction with a qualitative VLM assessment of the scene layout"},
  {"priority": "LOW", "description": "Check that 3D centroids are computed using median/confidence filtering to reduce noise"}
]