ViewSpatial — Gemma4-31B — sample 5116

Task Analysis

The objective is to determine the location of a "box" relative to a specific person-centric perspective: "positioned at sink facing counter." This is an object-perspective spatial localization task.

Coordinate System Resolution: The question establishes a local coordinate system centered at the sink with a primary axis (the "forward" direction) defined by the vector from the sink to the counter.

• Front: The direction from the sink toward the counter.
• Back: The direction opposite to the counter.
• Right: 90 degrees clockwise from the forward direction (relative to the world's vertical axis).
• Left: 90 degrees counter-clockwise from the forward direction.

The target variable is the relative position of the box within this local frame (e.g., "back-left").

Information Needs

To answer this quantitatively, I need:

1. 3D positions (World Space): The centroids of the sink, the counter (specifically the part the person would face), and the box.
2. Scene Geometry: A 3D reconstruction to ensure metric consistency and to derive the world-up vector for calculating the local "right/left" axes.
3. Visual Confirmation: Verification that the identified "sink," "counter," and "box" are the correct objects in the scene.

Computation Plan

1. Visual Identification:

   • Use show(InputImages) to inspect the scene and identify the frames where the sink, counter, and box are most clearly visible.
   • Use vlm.ask_with_thinking to confirm the identities and general relative layout of the sink, counter, and box across the 5 frames.

2. 3D Reconstruction:

   • Perform a full scene reconstruction using recon = tools.Reconstruct.Reconstruct(InputImages).

3. Object Segmentation:

   • For the sink, counter, and box, use tools.SAM3.segment_image_by_text on the most informative frames.
   • If text segmentation fails or is ambiguous (e.g., multiple boxes), use vlm.locate to get bounding boxes and then tools.SAM3.segment_image_by_box.
   • Programmatically verify that the masks are non-empty and visually verify them using seg.visualize() and show().

4. Geometric Computation:

   • Extract 3D centroids using seg.get_centroid_3d(recon, ...) for:
     • $P_{sink}$ (Position of the sink)
     • $P_{counter}$ (Position of the counter area facing the sink)
     • $P_{box}$ (Position of the box)
   • Define the local coordinate system:
     • Forward Vector: $\vec{v}{fwd} = \text{normalize}(P{counter} - P_{sink})$
     • World Up: $\vec{v}_{up} = [0, 1, 0]$ (from Reconstruct convention)
     • Right Vector: $\vec{v}{right} = \text{normalize}(\vec{v}{fwd} \times \vec{v}_{up})$
     • Left Vector: $\vec{v}{left} = -\vec{v}{right}$
     • Back Vector: $\vec{v}{back} = -\vec{v}{fwd}$
   • Compute the relative vector to the box: $\vec{v}{box_rel} = P{box} - P_{sink}$
   • Project $\vec{v}_{box_rel}$ onto the local axes:
     • $dist_{fwd} = \vec{v}{box_rel} \cdot \vec{v}{fwd}$
     • $dist_{right} = \vec{v}{box_rel} \cdot \vec{v}{right}$

5. Relative Position Mapping:

   • If $dist_{fwd} < 0$ and $dist_{right} < 0 \rightarrow$ back-left (Option A)
   • If $dist_{fwd} < 0$ and $dist_{right} \approx 0 \rightarrow$ back (Option B)
   • If $dist_{fwd} > 0$ and $dist_{right} < 0 \rightarrow$ front-left (Option C)
   • If $dist_{right} > 0 \rightarrow$ right (Option D)

6. Cross-Validation:

   • Render a BEV plot using recon.render_bev(masks=seg) containing all three objects.
   • Visually verify that the relative positions in the BEV plot match the computed dot products.

Verification Checklist

[
  {"priority": "HIGH", "description": "Verify that the segmented 'sink', 'counter', and 'box' are the correct objects via visual inspection of masks."},
  {"priority": "HIGH", "description": "Ensure the 'facing' vector is correctly calculated as Sink -> Counter."},
  {"priority": "MEDIUM", "description": "Check that 3D centroids are not NaN and are physically plausible within the scene scale."},
  {"priority": "MEDIUM", "description": "Cross-reference the numerical result (dot products) with the BEV visualization."}
]

Fallbacks

• Ambiguous Counter: If the "counter" is a large L-shaped surface, I will use vlm.locate to find the specific point on the counter directly across from the sink to define the facing vector.
• Segmentation Failure: If SAM3 fails for any object, I will use vlm.locate for a center point and tools.SAM3.segment_image_by_points.
• Reconstruction Noise: If the 3D centroids seem unstable, I will average the centroids across multiple frames where the objects are visible.