vision_calibration_optim/problems/

handeye.rs

//! Hand-eye calibration for robot-mounted cameras.
//!
//! Default optimization state (fixed target):
//! - per-camera intrinsics and distortion
//! - per-camera extrinsics (camera-to-rig)
//! - hand-eye transform (mode-dependent; see `HandEyeInit::handeye`)
//! - fixed target pose (mode-dependent; see `HandEyeInit::target_poses`)
//! - optional per-view robot pose corrections delta_i in se(3), with zero-mean priors
//!
//! Transform chain (eye-in-hand):
//! `T_C_T_i = (T_B_E_i * X)^-1 * Y` where `X` is hand-eye and `Y` is target in base.
//! With robot refinement: `T_B_E_i_corr = exp(delta_i) * T_B_E_i` (left-multiply).
//!
//! Residuals:
//! - reprojection errors for observed target points using the robot pose chain
//! - optional priors on delta_i (anisotropic rotation/translation sigmas)
//! - when delta_i are enabled, delta_0 is fixed to zero to remove gauge freedom
//!
//! Legacy mode can relax per-view target poses, but that is discouraged for a
//! physically fixed target because it weakens hand-eye observability.

use crate::Error;
use crate::backend::{BackendKind, BackendSolveOptions, SolveReport, solve_with_backend};
use crate::ir::{
    FactorKind, FixedMask, HandEyeMode, ManifoldKind, ProblemIR, ResidualBlock, RobustLoss,
};
use crate::params::distortion::{DISTORTION_DIM, pack_distortion, unpack_distortion};
use crate::params::intrinsics::{INTRINSICS_DIM, pack_intrinsics, unpack_intrinsics};
use crate::params::pose_se3::iso3_to_se3_dvec;
use anyhow::ensure;
type AnyhowResult<T> = anyhow::Result<T>;
use nalgebra::DVector;
use serde::{Deserialize, Serialize};
use std::collections::HashMap;
use vision_calibration_core::{
    CameraFixMask, Iso3, PinholeCamera, Real, RigDataset, RigView, make_pinhole_camera,
};

/// Per-view robot metadata required by hand-eye calibration.
#[derive(Debug, Clone, Serialize, Deserialize)]
pub struct RobotPoseMeta {
    /// Gripper pose expressed in the robot base frame (T_B_G).
    #[serde(alias = "robot_pose")]
    pub base_se3_gripper: Iso3,
}

/// Dataset wrapper for hand-eye optimization.
#[derive(Debug, Clone, Serialize, Deserialize)]
pub struct HandEyeDataset {
    /// Multi-camera observations with robot metadata.
    pub data: RigDataset<RobotPoseMeta>,
    /// Hand-eye mode controlling transform chain.
    pub mode: HandEyeMode,
}

impl HandEyeDataset {
    /// Create dataset from views.
    pub fn new(
        views: Vec<RigView<RobotPoseMeta>>,
        num_cameras: usize,
        mode: HandEyeMode,
    ) -> AnyhowResult<Self> {
        ensure!(!views.is_empty(), "need at least one view");
        for (idx, view) in views.iter().enumerate() {
            ensure!(
                view.obs.cameras.len() == num_cameras,
                "view {} has {} cameras, expected {}",
                idx,
                view.obs.cameras.len(),
                num_cameras
            );
        }
        Ok(Self {
            data: RigDataset { views, num_cameras },
            mode,
        })
    }

    /// Number of views.
    pub fn num_views(&self) -> usize {
        self.data.views.len()
    }
}

/// Initial values for hand-eye calibration.
///
/// - `cam_to_rig`: camera pose in the rig frame (`T_C_R`)
/// - `handeye`:
///   - `EyeInHand`: gripper pose in the rig frame (`T_G_R`)
///   - `EyeToHand`: rig pose in the base frame (`T_R_B`)
/// - `target_poses`: fixed target pose(s) depending on the selected mode
#[derive(Debug, Clone, Serialize, Deserialize)]
pub struct HandEyeParams {
    /// Per-camera intrinsics and distortion.
    pub cameras: Vec<PinholeCamera>,
    /// Per-camera extrinsics (camera-to-rig transforms).
    pub cam_to_rig: Vec<Iso3>,
    /// Hand-eye transform (mode-dependent).
    ///
    /// - `EyeInHand`: `handeye = gripper_from_rig` (`T_G_R`)
    /// - `EyeToHand`: `handeye = rig_from_base` (`T_R_B`)
    pub handeye: Iso3,
    /// Calibration target poses.
    ///
    /// - Default (fixed target):
    ///   - `EyeInHand`: the first pose is used as the initial `base_from_target` (`T_B_T`)
    ///   - `EyeToHand`: the first pose is used as the initial `gripper_from_target` (`T_G_T`)
    /// - Legacy (`relax_target_poses = true`): one pose per view is required.
    pub target_poses: Vec<Iso3>,
}

/// Solve options for hand-eye calibration.
#[derive(Debug, Clone, Serialize, Deserialize)]
pub struct HandEyeSolveOptions {
    /// Robust loss applied to reprojection residuals.
    pub robust_loss: RobustLoss,

    /// Default mask for fixing camera parameters (applied to all cameras).
    pub default_fix: CameraFixMask,
    /// Optional per-camera overrides (None = use default_fix).
    pub camera_overrides: Vec<Option<CameraFixMask>>,
    /// Per-camera extrinsics masking (length must match num_cameras).
    pub fix_extrinsics: Vec<bool>,
    /// Fix hand-eye transform (for testing with known hand-eye).
    pub fix_handeye: bool,
    /// View indices to fix (legacy per-view target mode only).
    pub fix_target_poses: Vec<usize>,
    /// Legacy mode: relax per-view target poses instead of a fixed target.
    pub relax_target_poses: bool,
    /// Refine robot poses with per-view se(3) corrections and strong priors.
    ///
    /// When enabled, delta_0 is fixed to zero for gauge consistency.
    pub refine_robot_poses: bool,
    /// Robot rotation prior sigma (radians).
    pub robot_rot_sigma: Real,
    /// Robot translation prior sigma (meters).
    pub robot_trans_sigma: Real,
}

impl Default for HandEyeSolveOptions {
    fn default() -> Self {
        Self {
            robust_loss: RobustLoss::None,
            default_fix: CameraFixMask::default(), // k3 fixed by default
            camera_overrides: Vec::new(),
            fix_extrinsics: Vec::new(),
            fix_handeye: false,
            fix_target_poses: Vec::new(),
            relax_target_poses: false,
            refine_robot_poses: false,
            robot_rot_sigma: std::f64::consts::PI / 360.0, // 0.5 deg
            robot_trans_sigma: 1.0e-3,                     // 1 mm
        }
    }
}

/// Result of hand-eye calibration.
#[derive(Debug, Clone, Serialize, Deserialize)]
pub struct HandEyeEstimate {
    /// Refined hand-eye parameters.
    pub params: HandEyeParams,
    /// Backend solve report.
    pub report: SolveReport,
    /// Optional per-view robot pose deltas (se(3) tangent, `[rx, ry, rz, tx, ty, tz]`).
    pub robot_deltas: Option<Vec<[Real; 6]>>,
    /// Mean reprojection error in pixels (computed post-optimization).
    pub mean_reproj_error: f64,
    /// Per-camera reprojection errors in pixels.
    pub per_cam_reproj_errors: Vec<f64>,
}

/// Optimize hand-eye calibration using specified backend.
///
/// # Errors
///
/// Returns [`Error`] if IR construction or solver backend fails.
pub fn optimize_handeye(
    dataset: HandEyeDataset,
    initial: HandEyeParams,
    opts: HandEyeSolveOptions,
    backend_opts: BackendSolveOptions,
) -> Result<HandEyeEstimate, Error> {
    let (ir, initial_map) = build_handeye_ir(&dataset, &initial, &opts)?;
    let solution = solve_with_backend(BackendKind::TinySolver, &ir, &initial_map, &backend_opts)?;

    // Extract per-camera calibrated parameters
    let cameras = (0..dataset.data.num_cameras)
        .map(|cam_idx| {
            let intrinsics = unpack_intrinsics(
                solution
                    .params
                    .get(&format!("cam/{}", cam_idx))
                    .unwrap()
                    .as_view(),
            )?;
            let distortion = unpack_distortion(
                solution
                    .params
                    .get(&format!("dist/{}", cam_idx))
                    .unwrap()
                    .as_view(),
            )?;
            Ok(make_pinhole_camera(intrinsics, distortion))
        })
        .collect::<Result<Vec<_>, Error>>()?;

    // Extract extrinsics
    let cam_to_rig = (0..dataset.data.num_cameras)
        .map(|i| {
            let key = format!("extr/{}", i);
            crate::params::pose_se3::se3_dvec_to_iso3(solution.params.get(&key).unwrap().as_view())
        })
        .collect::<Result<Vec<_>, Error>>()?;

    // Extract hand-eye transform
    let handeye = crate::params::pose_se3::se3_dvec_to_iso3(
        solution.params.get("handeye").unwrap().as_view(),
    )?;

    // Extract target poses
    let target_poses = if opts.relax_target_poses {
        (0..dataset.num_views())
            .map(|i| {
                let key = format!("target/{}", i);
                crate::params::pose_se3::se3_dvec_to_iso3(
                    solution.params.get(&key).unwrap().as_view(),
                )
            })
            .collect::<Result<Vec<_>, Error>>()?
    } else {
        let target_pose = crate::params::pose_se3::se3_dvec_to_iso3(
            solution.params.get("target").unwrap().as_view(),
        )?;
        vec![target_pose; dataset.num_views()]
    };

    let robot_deltas = if opts.refine_robot_poses {
        let mut deltas = Vec::with_capacity(dataset.num_views());
        for i in 0..dataset.num_views() {
            let key = format!("robot_delta/{}", i);
            let delta_vec = solution.params.get(&key).unwrap();
            deltas.push([
                delta_vec[0],
                delta_vec[1],
                delta_vec[2],
                delta_vec[3],
                delta_vec[4],
                delta_vec[5],
            ]);
        }
        Some(deltas)
    } else {
        None
    };

    // Compute reprojection error
    let params = HandEyeParams {
        cameras,
        cam_to_rig,
        handeye,
        target_poses,
    };
    let (mean_reproj_error, per_cam_reproj_errors) =
        compute_handeye_reproj_error(&dataset, &params, robot_deltas.as_ref());

    Ok(HandEyeEstimate {
        params,
        report: solution.solve_report,
        robot_deltas,
        mean_reproj_error,
        per_cam_reproj_errors,
    })
}

/// Compute per-camera reprojection error for hand-eye calibration result.
///
/// Returns (mean_error, per_camera_errors).
fn compute_handeye_reproj_error(
    dataset: &HandEyeDataset,
    params: &HandEyeParams,
    robot_deltas: Option<&Vec<[Real; 6]>>,
) -> (f64, Vec<f64>) {
    use crate::ir::HandEyeMode;
    use nalgebra::{UnitQuaternion, Vector3};

    let num_cameras = dataset.data.num_cameras;
    let mut per_cam_sum = vec![0.0f64; num_cameras];
    let mut per_cam_count = vec![0usize; num_cameras];

    // Precompute cam_se3_rig transforms (inverse of cam_to_rig)
    let cam_se3_rig: Vec<Iso3> = params.cam_to_rig.iter().map(|t| t.inverse()).collect();

    // handeye_inv = handeye^-1
    let handeye_inv = params.handeye.inverse();

    // target_pose is assumed to be the first (and only) target pose for fixed-target mode
    let target_pose = params
        .target_poses
        .first()
        .cloned()
        .unwrap_or(Iso3::identity());

    for (view_idx, view) in dataset.data.views.iter().enumerate() {
        let robot_pose = view.meta.base_se3_gripper;

        // Apply robot delta if available
        let robot_pose = if let Some(deltas) = robot_deltas {
            let delta = &deltas[view_idx];
            let rot_vec = Vector3::new(delta[0], delta[1], delta[2]);
            let trans_vec = Vector3::new(delta[3], delta[4], delta[5]);
            let angle = rot_vec.norm();
            let delta_rot = if angle > 1e-12 {
                UnitQuaternion::from_axis_angle(&nalgebra::Unit::new_normalize(rot_vec), angle)
            } else {
                UnitQuaternion::identity()
            };
            let delta_iso = Iso3::from_parts(nalgebra::Translation3::from(trans_vec), delta_rot);
            delta_iso * robot_pose
        } else {
            robot_pose
        };

        for (cam_idx, cam_obs) in view.obs.cameras.iter().enumerate() {
            let Some(obs) = cam_obs else {
                continue;
            };
            let camera = &params.cameras[cam_idx];

            for (pt3, pt2) in obs.points_3d.iter().zip(obs.points_2d.iter()) {
                // Compute point in camera frame using hand-eye transform chain
                let p_camera = match dataset.mode {
                    HandEyeMode::EyeInHand => {
                        // target -> base -> gripper -> rig -> camera
                        let p_base = target_pose.transform_point(pt3);
                        let p_gripper = robot_pose.inverse_transform_point(&p_base);
                        let p_rig = handeye_inv.transform_point(&p_gripper);
                        cam_se3_rig[cam_idx].transform_point(&p_rig)
                    }
                    HandEyeMode::EyeToHand => {
                        // target -> gripper -> base -> rig -> camera
                        let p_gripper = target_pose.transform_point(pt3);
                        let p_base = robot_pose.transform_point(&p_gripper);
                        let p_rig = params.handeye.transform_point(&p_base);
                        cam_se3_rig[cam_idx].transform_point(&p_rig)
                    }
                };

                // Project point
                if let Some(proj) = camera.project_point_c(&p_camera.coords) {
                    let err = (proj - *pt2).norm();
                    per_cam_sum[cam_idx] += err;
                    per_cam_count[cam_idx] += 1;
                }
            }
        }
    }

    // Compute per-camera mean errors
    let per_cam_reproj_errors: Vec<f64> = per_cam_sum
        .iter()
        .zip(per_cam_count.iter())
        .map(|(&s, &c)| if c > 0 { s / c as f64 } else { 0.0 })
        .collect();

    // Compute overall mean
    let total_sum: f64 = per_cam_sum.iter().sum();
    let total_count: usize = per_cam_count.iter().sum();
    let mean_reproj_error = if total_count > 0 {
        total_sum / total_count as f64
    } else {
        0.0
    };

    (mean_reproj_error, per_cam_reproj_errors)
}

/// Build IR for hand-eye calibration.
///
/// State vector:
/// - intrinsics/distortion, extrinsics, hand-eye transform
/// - target pose (fixed by default, per-view in legacy mode)
/// - optional per-view robot pose deltas (se(3) tangent)
///
/// Residuals:
/// - per-point reprojection error using robot pose measurements
/// - optional zero-mean priors on robot pose deltas
fn build_handeye_ir(
    dataset: &HandEyeDataset,
    initial: &HandEyeParams,
    opts: &HandEyeSolveOptions,
) -> AnyhowResult<(ProblemIR, HashMap<String, DVector<f64>>)> {
    ensure!(
        initial.cameras.len() == dataset.data.num_cameras,
        "intrinsics count {} != num_cameras {}",
        initial.cameras.len(),
        dataset.data.num_cameras
    );
    ensure!(
        initial.cam_to_rig.len() == dataset.data.num_cameras,
        "cam_to_rig count {} != num_cameras {}",
        initial.cam_to_rig.len(),
        dataset.data.num_cameras
    );
    ensure!(
        !initial.target_poses.is_empty(),
        "target_poses must contain at least one pose"
    );
    if opts.relax_target_poses {
        ensure!(
            initial.target_poses.len() == dataset.num_views(),
            "target_poses count {} != num_views {}",
            initial.target_poses.len(),
            dataset.num_views()
        );
    }
    ensure!(
        opts.relax_target_poses || opts.fix_target_poses.is_empty(),
        "fix_target_poses is only supported when relax_target_poses is true"
    );
    if opts.refine_robot_poses {
        ensure!(
            opts.robot_rot_sigma > 0.0,
            "robot_rot_sigma must be positive"
        );
        ensure!(
            opts.robot_trans_sigma > 0.0,
            "robot_trans_sigma must be positive"
        );
    }

    let mut ir = ProblemIR::new();
    let mut initial_map = HashMap::new();

    // 1. Per-camera intrinsics blocks
    let mut cam_ids = Vec::new();
    for cam_idx in 0..dataset.data.num_cameras {
        let cam_fix = opts
            .camera_overrides
            .get(cam_idx)
            .copied()
            .flatten()
            .unwrap_or(opts.default_fix);
        let fixed = cam_fix.intrinsics.to_indices();
        let fixed_mask = FixedMask::fix_indices(&fixed);

        let key = format!("cam/{}", cam_idx);
        let cam_id = ir.add_param_block(
            &key,
            INTRINSICS_DIM,
            ManifoldKind::Euclidean,
            fixed_mask,
            None,
        );
        cam_ids.push(cam_id);
        initial_map.insert(key, pack_intrinsics(&initial.cameras[cam_idx].k)?);
    }

    // 2. Per-camera distortion blocks
    let mut dist_ids = Vec::new();
    for cam_idx in 0..dataset.data.num_cameras {
        let cam_fix = opts
            .camera_overrides
            .get(cam_idx)
            .copied()
            .flatten()
            .unwrap_or(opts.default_fix);
        let fixed = cam_fix.distortion.to_indices();
        let fixed_mask = FixedMask::fix_indices(&fixed);

        let key = format!("dist/{}", cam_idx);
        let dist_id = ir.add_param_block(
            &key,
            DISTORTION_DIM,
            ManifoldKind::Euclidean,
            fixed_mask,
            None,
        );
        dist_ids.push(dist_id);
        initial_map.insert(key, pack_distortion(&initial.cameras[cam_idx].dist));
    }

    // 3. Per-camera extrinsics
    let mut extr_ids = Vec::new();
    for cam_idx in 0..dataset.data.num_cameras {
        let fixed = if opts.fix_extrinsics.get(cam_idx).copied().unwrap_or(false) {
            FixedMask::all_fixed(7)
        } else {
            FixedMask::all_free()
        };
        let key = format!("extr/{}", cam_idx);
        let id = ir.add_param_block(&key, 7, ManifoldKind::SE3, fixed, None);
        extr_ids.push(id);
        initial_map.insert(key, iso3_to_se3_dvec(&initial.cam_to_rig[cam_idx]));
    }

    // 4. Hand-eye transform
    let handeye_fixed = if opts.fix_handeye {
        FixedMask::all_fixed(7)
    } else {
        FixedMask::all_free()
    };
    let handeye_id = ir.add_param_block("handeye", 7, ManifoldKind::SE3, handeye_fixed, None);
    initial_map.insert("handeye".to_string(), iso3_to_se3_dvec(&initial.handeye));

    // 5. Target pose (fixed by default) + residuals
    let target_id = if opts.relax_target_poses {
        None
    } else {
        let target_seed = initial.target_poses[0];
        let id = ir.add_param_block("target", 7, ManifoldKind::SE3, FixedMask::all_free(), None);
        initial_map.insert("target".to_string(), iso3_to_se3_dvec(&target_seed));
        Some(id)
    };

    let robot_prior_sqrt_info = if opts.refine_robot_poses {
        let rot = 1.0 / opts.robot_rot_sigma;
        let trans = 1.0 / opts.robot_trans_sigma;
        [rot, rot, rot, trans, trans, trans]
    } else {
        [0.0; 6]
    };

    for (view_idx, view) in dataset.data.views.iter().enumerate() {
        let target_id = if opts.relax_target_poses {
            let fixed = if opts.fix_target_poses.contains(&view_idx) {
                FixedMask::all_fixed(7)
            } else {
                FixedMask::all_free()
            };
            let key = format!("target/{}", view_idx);
            let target_id = ir.add_param_block(&key, 7, ManifoldKind::SE3, fixed, None);
            initial_map.insert(key, iso3_to_se3_dvec(&initial.target_poses[view_idx]));
            target_id
        } else {
            target_id.expect("target id should be set for fixed-target mode")
        };

        let robot_delta_id = if opts.refine_robot_poses {
            let fixed = if view_idx == 0 {
                FixedMask::all_fixed(6)
            } else {
                FixedMask::all_free()
            };
            let key = format!("robot_delta/{}", view_idx);
            let id = ir.add_param_block(&key, 6, ManifoldKind::Euclidean, fixed, None);
            initial_map.insert(key, DVector::from_element(6, 0.0));
            let prior = ResidualBlock {
                params: vec![id],
                loss: RobustLoss::None,
                factor: FactorKind::Se3TangentPrior {
                    sqrt_info: robot_prior_sqrt_info,
                },
                residual_dim: 6,
            };
            ir.add_residual_block(prior);
            Some(id)
        } else {
            None
        };

        // Convert robot pose to SE3 array for factor
        let robot_se3 = iso3_to_se3_dvec(&view.meta.base_se3_gripper);
        let robot_se3_array: [f64; 7] = [
            robot_se3[0],
            robot_se3[1],
            robot_se3[2],
            robot_se3[3],
            robot_se3[4],
            robot_se3[5],
            robot_se3[6],
        ];

        // Add residuals for each camera observation
        for (cam_idx, cam_obs) in view.obs.cameras.iter().enumerate() {
            if let Some(obs) = cam_obs {
                for (pt_idx, (pw, uv)) in obs.points_3d.iter().zip(&obs.points_2d).enumerate() {
                    let residual = if let Some(robot_delta_id) = robot_delta_id {
                        ResidualBlock {
                            params: vec![
                                cam_ids[cam_idx],
                                dist_ids[cam_idx],
                                extr_ids[cam_idx],
                                handeye_id,
                                target_id,
                                robot_delta_id,
                            ],
                            loss: opts.robust_loss,
                            factor: FactorKind::ReprojPointPinhole4Dist5HandEyeRobotDelta {
                                pw: [pw.x, pw.y, pw.z],
                                uv: [uv.x, uv.y],
                                w: obs.weight(pt_idx),
                                base_to_gripper_se3: robot_se3_array,
                                mode: dataset.mode,
                            },
                            residual_dim: 2,
                        }
                    } else {
                        ResidualBlock {
                            params: vec![
                                cam_ids[cam_idx],
                                dist_ids[cam_idx],
                                extr_ids[cam_idx],
                                handeye_id,
                                target_id,
                            ],
                            loss: opts.robust_loss,
                            factor: FactorKind::ReprojPointPinhole4Dist5HandEye {
                                pw: [pw.x, pw.y, pw.z],
                                uv: [uv.x, uv.y],
                                w: obs.weight(pt_idx),
                                base_to_gripper_se3: robot_se3_array,
                                mode: dataset.mode,
                            },
                            residual_dim: 2,
                        }
                    };
                    ir.add_residual_block(residual);
                }
            }
        }
    }

    ir.validate()?;
    Ok((ir, initial_map))
}

#[cfg(test)]
mod tests {
    use super::*;
    use nalgebra::{Translation3, UnitQuaternion};
    use vision_calibration_core::{
        BrownConrady5, CorrespondenceView, FxFyCxCySkew, Pt2, Pt3, RigView, RigViewObs,
        make_pinhole_camera,
    };

    fn make_test_camera() -> PinholeCamera {
        make_pinhole_camera(
            FxFyCxCySkew {
                fx: 600.0,
                fy: 590.0,
                cx: 320.0,
                cy: 240.0,
                skew: 0.0,
            },
            BrownConrady5::default(),
        )
    }

    fn project_view(
        camera: &PinholeCamera,
        cam_se3_target: &Iso3,
        board_pts: &[Pt3],
    ) -> CorrespondenceView {
        let pixels: Vec<Pt2> = board_pts
            .iter()
            .map(|p| {
                let p_cam = cam_se3_target.transform_point(p);
                camera
                    .project_point_c(&p_cam.coords)
                    .expect("point should be in front of camera")
            })
            .collect();

        CorrespondenceView::new(board_pts.to_vec(), pixels).unwrap()
    }

    #[test]
    fn compute_reproj_error_matches_ground_truth_chain() {
        let camera = make_test_camera();
        let handeye = Iso3::identity(); // gripper and camera frames coincide
        let target_in_base =
            Iso3::from_parts(Translation3::new(0.0, 0.0, 1.0), UnitQuaternion::identity());

        // Simple square target
        let board_pts = vec![
            Pt3::new(0.0, 0.0, 0.0),
            Pt3::new(0.1, 0.0, 0.0),
            Pt3::new(0.1, 0.1, 0.0),
            Pt3::new(0.0, 0.1, 0.0),
        ];

        let robot_poses = [
            Iso3::identity(),
            Iso3::from_parts(
                Translation3::new(0.05, 0.0, 0.0),
                UnitQuaternion::identity(),
            ),
        ];

        let views: Vec<RigView<RobotPoseMeta>> = robot_poses
            .iter()
            .map(|robot_pose| {
                // Camera pose: T_C_T = (T_B_G * T_G_C)^-1 * T_B_T
                let cam_se3_target = (robot_pose * handeye).inverse() * target_in_base;
                let obs = project_view(&camera, &cam_se3_target, &board_pts);

                RigView {
                    meta: RobotPoseMeta {
                        base_se3_gripper: *robot_pose,
                    },
                    obs: RigViewObs {
                        cameras: vec![Some(obs)],
                    },
                }
            })
            .collect();

        let dataset = HandEyeDataset::new(views, 1, HandEyeMode::EyeInHand).unwrap();
        let params = HandEyeParams {
            cameras: vec![camera],
            cam_to_rig: vec![Iso3::identity()],
            handeye,
            target_poses: vec![target_in_base],
        };

        let (mean, per_cam) = compute_handeye_reproj_error(&dataset, &params, None);
        assert!(mean < 1e-9, "mean reproj err too large: {}", mean);
        assert!(
            per_cam[0] < 1e-9,
            "per-cam reproj err too large: {}",
            per_cam[0]
        );
    }
}