Highlights / VSTI-Bench / sample 4387

VSTI-Bench — Gemma4-31B — sample 4387

Keyframes
Question
During the sequence between frame 16 and frame 31 of 32, what was the primary consistent direction of the camera's movement relative to its orientation at the start? The options are Forward, Right, Backward, and Left. A. Forward B. Right C. Backward D. Left
Ground truth A
SpatialClaw A ✓
Agent wins

No-tool Baseline

✗ Incorrect

To determine the primary consistent direction of the camera's movement between frame 16 and frame 31 of 32, let's analyze the sequence of images:

  1. Frame 16 to 21: The camera is positioned facing a brown door with a black and grey backpack hanging on it. There is very little lateral movement during this short interval.
  2. Frame 22 to 27: The camera begins to move and pan toward the right side of the room. We start to see a white sink and a mirror appearing on the right side of the frame.
  3. Frame 28 to 31: The camera continues its rightward movement, panning across the room. By frame 31, the sink is on the left and the toilet (which was seen at the very beginning of the video) has come back into view on the right side of the frame.

Throughout this sequence, the camera consistently shifts its perspective from the door on the left toward the fixtures on the right side of the restroom.

The primary consistent direction of the camera's movement is to the right.

B

Single-pass code

✗ Incorrect
Purpose
Determine the primary consistent direction of the camera's movement between frame 16 and frame 31 of 32.
Reasoning
1. **Frame Conversion**: I will convert the relative frame indices (16 and 31 of 32) to absolute video frame indices and find the corresponding indices in `InputImages`. 2. **3D Reconstruction**: I will use `tools.Reconstruct` on a sampled range of frames between these two points to get the camera's trajectory. 3. **Directional Analysis**: - I'll identify the camera's position and orientation at the start frame (frame 16). - I'll compute the displacement vector from the start position to the end position (frame 31). - I'll project this displacement vector onto the start camera's local axes: forward (Z), right (X). - The axis with the largest absolute projection will determine the primary direction (Forward, Backward, Right, or Left). 4. **Visual Confirmation**: I'll inspect the key frames. At frame 16, the camera is facing the door. By frame 31, the camera has moved back towards the sink and toilet. Since the sink/toilet are opposite the door, moving from the door back to the sink/toilet while facing the door constitutes "Backward" movement.
Next Goal
Execute the reconstruction and compute the movement vector.
Code
import numpy as np

# 1. Convert relative frames to video frame indices
N = 32
f1_rel = 16
f2_rel = 31

fraction1 = (f1_rel - 1) / (N - 1)
target_v1 = int(round(fraction1 * (Metadata.total_frames - 1)))
fraction2 = (f2_rel - 1) / (N - 1)
target_v2 = int(round(fraction2 * (Metadata.total_frames - 1)))

# Find closest indices in InputImages
i_start = min(range(len(InputImages)), key=lambda j: abs(InputImages[j].frame_index - target_v1))
i_end = min(range(len(InputImages)), key=lambda j: abs(InputImages[j].frame_index - target_v2))

print(f"Start: relative {f1_rel}, video {target_v1}, InputImages index {i_start}")
print(f"End: relative {f2_rel}, video {target_v2}, InputImages index {i_end}")

# 2. Reconstruct camera path
# Sample frames for reconstruction to stay under 64 frame limit
step = max(1, (i_end - i_start) // 31)
frames_to_recon = InputImages[i_start : i_end + 1 : step]
recon = tools.Reconstruct.Reconstruct(frames_to_recon)

# 3. Analyze movement relative to start orientation
# Start frame data
start_frame_idx = InputImages[i_start].frame_index
pose_start = recon.extrinsics[start_frame_idx]
pos_start = pose_start[:3, 3]
cam_fwd = pose_start[:3, 2]   # +Z
cam_right = pose_start[:3, 0] # +X

# End frame data
end_frame_idx = InputImages[i_end].frame_index
pose_end = recon.extrinsics[end_frame_idx]
pos_end = pose_end[:3, 3]

# Displacement vector
vec = pos_end - pos_start
dist = np.linalg.norm(vec)
print(f"Total displacement: {dist:.3f}m")

# Projections
dot_fwd = np.dot(vec, cam_fwd)
dot_right = np.dot(vec, cam_right)

print(f"Forward projection: {dot_fwd:.3f}m")
print(f"Right projection: {dot_right:.3f}m")

# Determine primary direction
if abs(dot_fwd) > abs(dot_right):
    direction = "Forward" if dot_fwd > 0 else "Backward"
else:
    direction = "Right" if dot_right > 0 else "Left"

print(f"Primary direction: {direction}")

# Map direction to option
mapping = {"Forward": "A", "Right": "B", "Backward": "C", "Left": "D"}
ReturnAnswer(mapping[direction])
Output
Start: relative 16, video 757, InputImages index 757
End: relative 31, video 1515, InputImages index 1515
Error
---------------------------------------------------------------------------
KeyError                                  Traceback (most recent call last)
Cell In[22], line 36
     34 # End frame data
     35 end_frame_idx = InputImages[i_end].frame_index
---> 36 pose_end = recon.extrinsics[end_frame_idx]
     37 pos_end = pose_end[:3, 3]
     39 # Displacement vector

File SpatialAgent/spatial_agent/kernel_types/per_frame_types.py:451, in PerFrameExtrinsics.__getitem__(self, frame_idx)
    449 def __getitem__(self, frame_idx: int) -> np.ndarray:
    450     """Get ``(4, 4)`` camera-to-world pose by absolute frame index."""
--> 451     local = self.get_by_frame_index(frame_idx)
    452     return self.camera_poses[local]

File SpatialAgent/spatial_agent/kernel_types/per_frame_types.py:69, in PerFrameData.get_by_frame_index(self, abs_frame_idx)
     64     if abs_frame_idx == 0 and 0 not in avail:
     65         hint = (
     66             f"\n  Hint: Did you mean frame={avail[0]}? "
     67             f"Use ABSOLUTE frame indices (from seg.frame_indices), not 0-based local indices."
     68         )
---> 69     raise KeyError(
     70         f"Frame {abs_frame_idx} not found in {avail}. "
     71         f"Available frames: {avail}{hint}"
     72     )
     73 return self._frame_indices.index(abs_frame_idx)

KeyError: 'Frame 1515 not found in [757, 781, 805, 829, 853, 877, 901, 925, 949, 973, 997, 1021, 1045, 1069, 1093, 1117, 1141, 1165, 1189, 1213, 1237, 1261, 1285, 1309, 1333, 1357, 1381, 1405, 1429, 1453, 1477, 1501]. Available frames: [757, 781, 805, 829, 853, 877, 901, 925, 949, 973, 997, 1021, 1045, 1069, 1093, 1117, 1141, 1165, 1189, 1213, 1237, 1261, 1285, 1309, 1333, 1357, 1381, 1405, 1429, 1453, 1477, 1501]'
Final answer
C

Structured tool-call

✗ Incorrect
Plan

Task Analysis

The goal is to determine the primary consistent direction of the camera's movement (Forward, Right, Backward, or Left) between frame 16 and frame 31 of the 32 sampled frames, relative to the camera's orientation at the start of that sequence (frame 16).

Coordinate System Resolution: The question asks for movement relative to the camera's orientation at a specific point in time. This is a camera-relative 3D problem.

  • Reference Frame: The camera pose at frame 16 (index 15 of InputImages).
  • Reference Axes: The camera's local "forward" (+Z in camera space) and "right" (+X in camera space) vectors at frame 16, mapped into world space.
  • Movement: The displacement of the camera center from frame 16 to frame 31.

Information Needs

  1. Camera Trajectory: Precise 3D world positions of the camera for all frames in the range [16, 31].
  2. Reference Orientation: The rotation matrix (extrinsics) of the camera at frame 16 to define the local coordinate system.
  3. Temporal Trend: The sign and magnitude of the displacement projected onto the reference axes over the sequence.

Computation Plan

  1. 3D Reconstruction:

    • Use tools.Reconstruct.Reconstruct(InputImages) to get the camera poses and world coordinates for the entire sequence. Since there are only 32 frames, this is within the 64-frame limit.

  2. Establish Reference Frame (Frame 16 / Index 15):

    • Identify the absolute frame index for frame 16: fi_start = InputImages.frame_indices[15].
    • Extract the camera-to-world matrix: pose_start = recon.extrinsics[fi_start].
    • Extract the world-space reference vectors:
      • cam_pos_start = pose_start[:3, 3]
      • cam_fwd_start = pose_start[:3, 2] (Forward vector)
      • cam_right_start = pose_start[:3, 0] (Right vector)

  3. Analyze Movement Sequence (Frames 16 to 31 / Indices 15 to 30):

    • For each index i from 15 to 30:
      • Get the absolute frame index: fi = InputImages.frame_indices[i].
      • Get the current camera position: cam_pos_t = recon.extrinsics[fi][:3, 3].
      • Calculate the displacement vector from the start: vec_t = cam_pos_t - cam_pos_start.
      • Project the displacement onto the reference axes:
        • proj_fwd = np.dot(vec_t, cam_fwd_start)
        • proj_right = np.dot(vec_t, cam_right_start)
      • Store proj_fwd and proj_right in arrays.

  4. Quantitative Evaluation:

    • Use tools.Graph.plot() to plot proj_fwd and proj_right over the sequence.
    • Analyze the trend:
      • Consistent increase in proj_fwd $\rightarrow$ Forward.
      • Consistent decrease in proj_fwd $\rightarrow$ Backward.
      • Consistent increase in proj_right $\rightarrow$ Right.
      • Consistent decrease in proj_right $\rightarrow$ Left.

  5. Visual Cross-Validation:

    • Render a Bird's Eye View (BEV) of the trajectory: recon.render_bev(ego_trajectory=True).
    • Use show() to inspect the BEV. Identify the camera position at index 15 and follow the trajectory to index 30.
    • Verify if the visual path matches the numerical projections (e.g., if the trajectory moves "forward" relative to the orientation of the camera at index 15).

Verification Checklist

[
  {"priority": "HIGH", "description": "Confirm that frame 16 (index 15) is used as the orientation reference for all projections"},
  {"priority": "HIGH", "description": "Verify that the camera-to-world matrix columns are correctly mapped to Right (+X) and Forward (+Z)"},
  {"priority": "MEDIUM", "description": "Cross-check the numerical dot-product trends with the visual camera path in the BEV render"},
  {"priority": "LOW", "description": "Ensure the reconstruction is stable and does not contain erratic pose jumps in the range [15, 30]"}
]

Fallbacks

  • Reconstruction Failure: If tools.Reconstruct produces noisy poses (detected via erratic jumps in the tools.Graph plots), I will use vlm.ask_with_thinking on a sampled set of frames (e.g., indices 15, 20, 25, 30) to qualitatively describe the camera's motion relative to the scene.
  • Ambiguous Motion: If the camera moves diagonally (e.g., both Forward and Right), I will compare the magnitudes of the total displacement along each axis to determine the "primary" direction.
Step 0
LLM · Tool Call
Purpose
Perform 3D reconstruction of the scene to obtain camera poses.
Reasoning
To determine camera movement relative to its starting orientation, I need the precise 3D world positions and orientations (extrinsics) of the camera for the frames in question. `tools.Reconstruct.Reconstruct` provides this data.
Next Goal
Establish the reference frame at index 15 (frame 16) and calculate the camera displacement projections.
Tool Call
{
  "tool": "tools.Reconstruct.Reconstruct",
  "args": {
    "frames": "InputImages[:32]"
  }
}
Step 1
LLM · Tool Call
Purpose
Visually inspect the camera trajectory in Bird's Eye View (BEV).
Reasoning
The BEV plot provides a top-down view of the camera's path. By observing the trajectory from the position at index 15 to index 30, I can qualitatively determine the primary direction of movement relative to the camera's heading at the start of that segment. This serves as a crucial sanity check before and alongside any quantitative calculations.
Next Goal
Analyze the BEV image and then perform a quantitative projection of the displacement vector from frame 16 to frame 31 onto the reference axes.
Tool Call
{
  "tool": "show",
  "args": {
    "image": "result_0.render_bev(ego_trajectory=True)"
  }
}
Execute
Output
 [image: show_0001]
show_0001
Step 2
LLM · Tool Call
Purpose
Quantitatively determine the camera's movement direction relative to its orientation at frame 16.
Reasoning
Visual inspection of the frames suggests the camera starts facing a door (frame 16) and ends up near a sink/toilet (frame 31), moving away from the door. To confirm this and determine if the primary movement is Forward, Backward, Left, or Right relative to the start, I will calculate the displacement vector from the camera position at index 15 to index 30 and project it onto the camera's local "forward" and "right" axes at index 15.
Next Goal
Compute the projections and determine the primary direction. **Tool Call (translated)**: ```python # I need to perform a calculation. Since I can't write free-form code with operators, # I'll use a tool if available or a sequence of tool calls. # Actually, the prompt says I cannot use operators like '+', '-', etc. # I must use tools.Geometry. # But I don't have a tool for 'vector subtraction' or 'dot product'. # Wait, tools.Geometry.euclidean_distance exists, but not dot product. # I will use vlm.ask_with_thinking to analyze the motion across the specific frames. ``` Actually, I can use `vlm.ask_with_thinking` on the frames to confirm the relative motion. Frames 16 to 31 are `InputImages[15:31]`.
Tool Call
{
  "tool": "vlm.ask_with_thinking",
  "args": {
    "visual_input": "InputImages[15:31]",
    "question": "In frame 16 (the first image), the camera is facing a door. By frame 31 (the last image), the camera has moved to a position near a sink and toilet. Relative to the camera's orientation in frame 16, did the camera primarily move Forward, Backward, Left, or Right?"
  }
}
Execute
Output
[VLM Q | thinking] In frame 16 (the first image), the camera is facing a door. By frame 31 (the last image), the camera has moved to a position near a sink and toilet. Relative to the camera's orientation in frame 16, did the camera primarily move Forward, Backward, Left, or Right?
[VLM A | thinking] Cannot determine from the images.
The provided images are all identical, showing no movement or a door in the first frame.
Step 3
LLM · Tool Call
Purpose
Determine the primary consistent direction of camera movement between frame 16 and frame 31.
Reasoning
1. **Analyze the scene layout**: Based on the provided key frames, the camera starts the video (frame 0) near a toilet and sink. By frame 16 (index 15), the camera has moved to a position where it is directly facing a door. By frame 31 (index 30), the camera has returned to the area near the sink and toilet. 2. **Establish the reference orientation**: At frame 16, the camera is facing the door. This direction (facing the door) defines the "Forward" axis for the movement sequence. 3. **Determine the displacement**: The camera moves from the door (frame 16) back toward the toilet/sink area (frame 31). 4. **Relate displacement to orientation**: Since the camera was facing the door at the start of the sequence and moved away from the door to return to its previous location, the primary direction of movement is opposite to its forward-facing orientation. 5. **Conclusion**: Movement opposite to the forward orientation is "Backward".
Next Goal
Submit the final answer.
Tool Call
{
  "tool": "ReturnAnswer",
  "args": {
    "answer": "C"
  }
}
Execute
Output
[ReturnAnswer] Answer submitted: C
Answer
C

SpaceTools

✗ Incorrect
Reasoning

To determine the primary consistent direction of the camera's movement between frame 16 and frame 31 of 32, we examine the sequence of images:

  1. Frame 16: The camera is facing a door with a backpack hanging on it.
  2. Frames 17-19: The camera shifts slightly, maintaining a view of the door and the wall.
  3. Frames 20-23: The camera pans and moves towards the right, bringing a white sink into view.
  4. Frames 24-25: The camera continues moving right, revealing the toilet area next to the sink.
  5. Frames 26-28: The camera moves further right/forward, showing the mirror and more of the wall.
  6. Frames 29-31: The camera completes a movement that brings the view back to the toilet and the dispenser on the wall, having moved generally in a rightward direction across the room relative to its starting orientation.

Looking at the progression from frame 16 (door) to frame 31 (toilet/dispenser), the camera consistently moves to the right side of the room.

The primary consistent direction of movement is Right.

B. Right

Final answer

To determine the primary consistent direction of the camera's movement between frame 16 and frame 31 of 32, we examine the sequence of images:

  1. Frame 16: The camera is facing a door with a backpack hanging on it.
  2. Frames 17-19: The camera shifts slightly, maintaining a view of the door and the wall.
  3. Frames 20-23: The camera pans and moves towards the right, bringing a white sink into view.
  4. Frames 24-25: The camera continues moving right, revealing the toilet area next to the sink.
  5. Frames 26-28: The camera moves further right/forward, showing the mirror and more of the wall.
  6. Frames 29-31: The camera completes a movement that brings the view back to the toilet and the dispenser on the wall, having moved generally in a rightward direction across the room relative to its starting orientation.

Looking at the progression from frame 16 (door) to frame 31 (toilet/dispenser), the camera consistently moves to the right side of the room.

The primary consistent direction of movement is Right.

B. Right

Final response

To determine the primary consistent direction of the camera's movement between frame 16 and frame 31 of 32, we examine the sequence of images:

  1. Frame 16: The camera is facing a door with a backpack hanging on it.
  2. Frames 17-19: The camera shifts slightly, maintaining a view of the door and the wall.
  3. Frames 20-23: The camera pans and moves towards the right, bringing a white sink into view.
  4. Frames 24-25: The camera continues moving right, revealing the toilet area next to the sink.
  5. Frames 26-28: The camera moves further right/forward, showing the mirror and more of the wall.
  6. Frames 29-31: The camera completes a movement that brings the view back to the toilet and the dispenser on the wall, having moved generally in a rightward direction across the room relative to its starting orientation.

Looking at the progression from frame 16 (door) to frame 31 (toilet/dispenser), the camera consistently moves to the right side of the room.

The primary consistent direction of movement is Right.

B. Right

SpatialClaw

✓ Correct
Plan

Task Analysis

The goal is to determine the primary consistent direction of the camera's movement between frame 16 and frame 31 of 32, relative to the camera's orientation at the start of that sequence (frame 16).

Coordinate System Resolution: The question asks for movement relative to the camera's orientation at the start. This requires a camera-relative 3D coordinate system anchored at the first frame of the sequence.

  • Forward: Along the camera's Z-axis (viewing direction) at frame 16.
  • Backward: Opposite to the camera's Z-axis at frame 16.
  • Right: Along the camera's X-axis at frame 16.
  • Left: Opposite to the camera's X-axis at frame 16.

The target variable is a categorical direction (Forward, Right, Backward, or Left).

Information Needs

  1. Frame Mapping: Conversion of "frame 16 of 32" and "frame 31 of 32" to absolute video frame indices and their corresponding indices in the InputImages list.
  2. Camera Poses: The 3D camera-to-world (c2w) matrices for the frames in the specified range to extract position and orientation.
  3. Trajectory Data: The sequence of 3D positions of the camera.
  4. Reference Vectors: The forward and right vectors of the camera at the start frame (frame 16).

Computation Plan

  1. Frame Identification:

    • Calculate the absolute video frame indices for "frame 16 of 32" and "frame 31 of 32" using the formula: fraction = (X - 1) / (32 - 1), target_video_frame = round(fraction * (Metadata.total_frames - 1)).
    • Identify the slice of InputImages whose frame_indices fall between these two absolute indices. Let this range be InputImages[idx_start : idx_end + 1].

  2. 3D Reconstruction:

    • Call recon = tools.Reconstruct.Reconstruct(InputImages[idx_start : idx_end + 1]) to obtain camera poses.

  3. Reference Frame Establishment:

    • Get the camera pose at the start frame: fi_start = recon.frame_indices[0].
    • Extract the reference position: pos_start = recon.extrinsics[fi_start][:3, 3].
    • Extract the reference orientation vectors:
      • fwd_start = recon.extrinsics[fi_start][:3, 2] (Z-axis)
      • right_start = recon.extrinsics[fi_start][:3, 0] (X-axis)

  4. Quantitative Trajectory Analysis:

    • For every frame fi in recon.frame_indices:
      • Get the current position: pos_current = recon.extrinsics[fi][:3, 3].
      • Calculate the displacement vector: vec = pos_current - pos_start.
      • Compute projections:
        • dot_fwd = np.dot(vec, fwd_start)
        • dot_right = np.dot(vec, right_start)
    • Store these values in arrays to analyze the trend.

  5. Direction Determination:

    • Compare the magnitudes and signs of the average or final dot_fwd and dot_right.
    • If dot_fwd is the dominant component and positive $\rightarrow$ Forward.
    • If dot_fwd is the dominant component and negative $\rightarrow$ Backward.
    • If dot_right is the dominant component and positive $\rightarrow$ Right.
    • If dot_right is the dominant component and negative $\rightarrow$ Left.

  6. Visual Verification:

    • Call recon.render_bev(ego_trajectory=True) to visualize the path.
    • Since the reconstruction is anchored to the first frame of the sequence, the BEV plot's world axes align with the start camera's orientation (specifically, the first camera looks toward -Z in the world frame).
    • Verify that the trajectory's primary direction in the BEV plot matches the numerical result.

Verification Checklist

[
  {"priority": "HIGH", "description": "Correctly map 'frame 16 of 32' and 'frame 31 of 32' to InputImages indices"},
  {"priority": "HIGH", "description": "Ensure the reference orientation (fwd/right vectors) is taken strictly from the start frame of the sequence"},
  {"priority": "MEDIUM", "description": "Cross-validate numerical dot products with the BEV trajectory visualization"},
  {"priority": "LOW", "description": "Check for significant camera rotation that might make 'consistent direction' ambiguous"}
]

Fallbacks

  • Poor Reconstruction: If the reconstruction fails or produces noisy poses (e.g., very small displacement), use vlm.ask_with_thinking on the frames in the range, asking specifically about the camera's movement relative to the first frame.
  • Ambiguous Motion: If the camera moves in a complex curve, calculate the net displacement vector from the first to the last frame to determine the primary overall direction.
Step 0
LLM
Purpose
Map the requested frame range ("frame 16 of 32" to "frame 31 of 32") to absolute video frame indices and identify the corresponding slice in `InputImages`.
Reasoning
The question uses a uniform sampling protocol (X of N). I must convert these relative indices into absolute video frame numbers based on the total number of frames in the video, and then locate the nearest available frames in the `InputImages` list to ensure I'm analyzing the correct temporal window.
Next Goal
Perform 3D reconstruction of the identified frame range to extract camera poses and trajectories.
Execute
Code
# Parameters from the question
X_start = 16
X_end = 31
N = 32

# Total frames in the video
total_frames = Metadata.total_frames

# Convert relative frames to absolute video frame indices
fraction_start = (X_start - 1) / (N - 1)
target_start = int(round(fraction_start * (total_frames - 1)))

fraction_end = (X_end - 1) / (N - 1)
target_end = int(round(fraction_end * (total_frames - 1)))

print(f"Target start video frame: {target_start}")
print(f"Target end video frame: {target_end}")

# Find the indices in InputImages that are closest to these target video frames
idx_start = min(range(len(InputImages)), key=lambda j: abs(InputImages[j].frame_index - target_start))
idx_end = min(range(len(InputImages)), key=lambda j: abs(InputImages[j].frame_index - target_end))

# Ensure indices are in the correct order and get the slice
if idx_start > idx_end:
    idx_start, idx_end = idx_end, idx_start

# We take the slice from idx_start to idx_end inclusive
frames_to_use = InputImages[idx_start : idx_end + 1]

print(f"InputImages index range: {idx_start} to {idx_end}")
print(f"Absolute video frame range: {InputImages[idx_start].frame_index} to {InputImages[idx_end].frame_index}")
print(f"Number of frames in slice: {len(frames_to_use)}")

# Visual check of the start and end frames of the sequence
show([InputImages[idx_start], InputImages[idx_end]])
Output
Target start video frame: 757
Target end video frame: 1515
InputImages index range: 757 to 1515
Absolute video frame range: 757 to 1515
Number of frames in slice: 759
 [image: show_0001]
show_0001
Step 1
LLM
Purpose
Perform 3D reconstruction of the camera trajectory between the identified frames.
Reasoning
To quantitatively determine the camera's movement direction, I need the 3D camera poses (position and orientation) over time. Since `tools.Reconstruct.Reconstruct` has a limit of 64 frames, I will subsample the 759 frames in the range [757, 1515] to a uniform set of 64 frames. This will provide a representative trajectory while staying within the tool's limits.
Next Goal
Extract the reference orientation from the first frame and compute the displacement projections (Forward/Right) for the rest of the trajectory.
Execute
Code
# Subsample frames to fit the 64-frame limit of tools.Reconstruct
num_to_sample = 64
indices = np.linspace(0, len(frames_to_use) - 1, num_to_sample, dtype=int)
subsampled_frames = [frames_to_use[i] for i in indices]

# Perform 3D reconstruction
recon = tools.Reconstruct.Reconstruct(subsampled_frames)

# Basic sanity check on reconstruction
print(f"Reconstructed {recon.num_frames} frames.")
print(f"Metric scale: {recon.metric_scale}")

# Visualize the trajectory in BEV to get a qualitative sense
# Since we have no masks, we use ego_trajectory=True to see the camera path
bev_vis = recon.render_bev(ego_trajectory=True)
show(bev_vis)
Output
Reconstructed 64 frames.
Metric scale: 1.515516996383667
 [image: show_0002]
show_0002
Step 2
LLM
Purpose
Quantitatively analyze the camera's movement direction relative to its initial orientation.
Reasoning
While the BEV plot qualitatively suggests a primary "Forward" motion, I must verify this with precise calculations. I will project the displacement of the camera from its starting position onto the starting camera's forward (Z-axis) and right (X-axis) vectors. This removes any ambiguity caused by camera rotation and provides a metric for "Forward", "Backward", "Left", and "Right" relative to the start.
Next Goal
Determine the primary direction based on the dominant projection and submit the final answer.
Execute
Code
# Reference frame: the first frame of the reconstructed sequence
fi_start = recon.frame_indices[0]
pose_start = recon.extrinsics[fi_start]
pos_start = pose_start[:3, 3]
fwd_start = pose_start[:3, 2]   # Camera forward vector (Z)
right_start = pose_start[:3, 0] # Camera right vector (X)

dot_fwd_list = []
dot_right_list = []

for fi in recon.frame_indices:
    pos_current = recon.extrinsics[fi][:3, 3]
    vec = pos_current - pos_start
    
    dot_fwd = np.dot(vec, fwd_start)
    dot_right = np.dot(vec, right_start)
    
    dot_fwd_list.append(dot_fwd)
    dot_right_list.append(dot_right)

dot_fwd_arr = np.array(dot_fwd_list)
dot_right_arr = np.array(dot_right_list)

print(f"Start position: {pos_start}")
print(f"Final displacement projection - Forward: {dot_fwd_arr[-1]:.3f}, Right: {dot_right_arr[-1]:.3f}")
print(f"Average displacement projection - Forward: {np.mean(dot_fwd_arr):.3f}, Right: {np.mean(dot_right_arr):.3f}")

# Plotting the projections over time to see the trend
fig, (ax1, ax2) = plt.subplots(2, 1, figsize=(8, 6), sharex=True)
ax1.plot(dot_fwd_arr, color='blue')
ax1.set_ylabel("Forward Projection")
ax1.grid(True)
ax2.plot(dot_right_arr, color='green')
ax2.set_ylabel("Right Projection")
ax2.set_xlabel("Sampled Frame Index")
ax2.grid(True)
plt.tight_layout()
plt.show()
Output
Start position: [0.15476985 1.30526135 0.5826965 ]
Final displacement projection - Forward: 1.164, Right: 0.411
Average displacement projection - Forward: 0.338, Right: -0.081
 [image: matplotlib figure]
matplotlib figure
Step 3
LLM
Purpose
Determine the primary consistent direction of the camera's movement based on the quantitative trajectory analysis.
Reasoning
1. **Reference Frame**: I established the coordinate system based on the camera's orientation at the start of the sequence (frame 16 of 32). 2. **Quantitative Evidence**: * The **Forward projection** (`dot_fwd`) shows a clear overall increasing trend, ending at approximately $1.164$ meters. * The **Right projection** (`dot_right`) oscillates and ends at a much smaller value of $0.411$ meters. * Comparing the final displacements, the forward component ($1.164$) is nearly 3 times larger than the right component ($0.411$). 3. **Visual Evidence**: The BEV trajectory plot clearly shows the camera moving primarily in the direction labeled "FORWARD (away from camera)". 4. **Consistency**: Both the numerical projections and the BEV visualization independently confirm that the dominant and most consistent direction of movement is Forward.
Next Goal
Submit the final answer.
Execute
Code
ReturnAnswer("A")
Output
[ReturnAnswer] Answer submitted: A
Answer
A
Evaluation
Ground truth: A · Agent: A