FoundationPose decoder: tf_to_center sign is inverted, causing 2*R*c translation error

Summary

In foundationpose_decoder.cpp, the tf_to_center translation sign is inverted compared to the original Python implementation, causing a systematic translation error of 2 * R * mesh_model_center in the output pose.

Root Cause

The mesh vertices are centered during loading by subtracting mesh_model_center:

// mesh_storage.cpp:210-212
vertices.push_back(mesh->mVertices[v].x - mesh_data_->mesh_model_center[0]);
vertices.push_back(mesh->mVertices[v].y - mesh_data_->mesh_model_center[1]);
vertices.push_back(mesh->mVertices[v].z - mesh_data_->mesh_model_center[2]);

The internal pose maps centered vertices to camera coordinates:

p_cam = R * v_centered + t = R * (v_original - c) + t = R * v_original + (t - R*c)

So the API pose translation should be t_api = t - R*c, requiring tf_to_center = [I | -c].

However, the decoder uses +mesh_model_center:

// foundationpose_decoder.cpp:173-176
// Add the distance from edge to the center because
Eigen::Matrix4f tf_to_center = Eigen::Matrix4f::Identity();
tf_to_center.block<3, 1>(0, 3) = mesh_data_ptr->mesh_model_center;  // should be negative
pose_matrix = pose_matrix * tf_to_center;

This produces t_api = t + R*c instead of t - R*c, introducing a 2*R*c offset.

Reference: Original Python Implementation

The official Python FoundationPose (estimater.py) correctly uses the negative sign:

# bundlesdf/foundation_pose/estimater.py
def get_tf_to_centered_mesh(self):
    tf_to_center = torch.eye(4, dtype=torch.float, device='cuda')
    tf_to_center[:3,3] = -torch.as_tensor(self.model_center, device='cuda', dtype=torch.float)  # negative
    return tf_to_center

Impact

• Translation error magnitude: 2 * ||mesh_model_center||
• For a mesh with bbox center at ~22mm from origin → ~44mm systematic error
• Error norm is constant across all scenes, but XYZ components vary with camera viewpoint (because of the R * factor)
• Rotation estimation is unaffected

Proposed Fix

- tf_to_center.block<3, 1>(0, 3) = mesh_data_ptr->mesh_model_center;
+ tf_to_center.block<3, 1>(0, 3) = -mesh_data_ptr->mesh_model_center;

Reproduction

Run FoundationPose on any mesh whose bounding box center is not at origin. Compare the C++ output pose with the Python estimater.py output on the same input. The translation will differ by 2 * R * mesh_model_center.