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//! This crate seamlessly plugs into `cv-core` and provides pinhole camera models with and without distortion correction. //! It can be used to convert image coordinates into real 3d direction vectors (called bearings) pointing towards where //! the light came from that hit that pixel. It can also be used to convert backwards from the 3d back to the 2d //! using the `uncalibrate` method from the [`cv_core::CameraModel`] trait. #![no_std] #[cfg(feature = "alloc")] extern crate alloc; mod essential; pub use essential::*; use cv_core::nalgebra::{Matrix3, Point2, Point3, Vector2, Vector3}; use cv_core::{ Bearing, CameraModel, CameraPoint, CameraToCamera, FeatureMatch, ImagePoint, KeyPoint, Pose, Projective, TriangulatorRelative, }; use derive_more::{AsMut, AsRef, Deref, DerefMut, From, Into}; use num_traits::Float; /// A point in normalized image coordinates. This keypoint has been corrected /// for distortion and normalized based on the camrea intrinsic matrix. /// Please note that the intrinsic matrix accounts for the natural focal length /// and any magnification to the image. Ultimately, the key points must be /// represented by their position on the camera sensor and normalized to the /// focal length of the camera. #[derive(Debug, Clone, Copy, PartialEq, PartialOrd, AsMut, AsRef, Deref, DerefMut, From, Into)] pub struct NormalizedKeyPoint(pub Point2<f64>); impl NormalizedKeyPoint { /// Tries to convert the [`CameraPoint`] into a [`NormalizedKeyPoint`], but it may fail /// in extreme conditions, in which case `None` is returned. pub fn from_camera_point(point: CameraPoint) -> Option<Self> { Point2::from_homogeneous(point.bearing_unnormalized()).map(Self) } /// Conceptually appends a `1.0` component to the normalized keypoint to create /// a [`CameraPoint`] on the virtual image plane and then multiplies /// the point by `depth`. This `z`/`depth` component must be the depth of /// the keypoint in the direction the camera is pointing from the /// camera's optical center. /// /// The `depth` is computed as the dot product of the unit camera norm /// with the vector that represents the position delta of the point from /// the camera. pub fn with_depth(self, depth: f64) -> CameraPoint { (self.coords * depth).push(depth).to_homogeneous().into() } /// Projects the keypoint out to the [`CameraPoint`] that is /// `distance` away from the optical center of the camera. This /// `distance` is defined as the norm of the vector that represents /// the position delta of the point from the camera. pub fn with_distance(self, distance: f64) -> CameraPoint { (distance * *self.bearing()).to_homogeneous().into() } /// Get the virtual image point as a [`Point3`]. /// /// The virtual image point is the point that is formed on the virtual /// image plane at a depth 1.0 in front of the camera. pub fn virtual_image_point(self) -> Point3<f64> { self.coords.push(1.0).into() } } impl Bearing for NormalizedKeyPoint { fn bearing_unnormalized(&self) -> Vector3<f64> { self.0.coords.push(1.0) } fn from_bearing_vector(bearing: Vector3<f64>) -> Self { Self((bearing.xy() / bearing.z).into()) } } /// This contains intrinsic camera parameters as per /// [this Wikipedia page](https://en.wikipedia.org/wiki/Camera_resectioning#Intrinsic_parameters). /// /// For a high quality camera, this may be sufficient to normalize image coordinates. /// Undistortion may also be necessary to normalize image coordinates. #[derive(Debug, Clone, Copy, PartialEq, PartialOrd)] pub struct CameraIntrinsics { pub focals: Vector2<f64>, pub principal_point: Point2<f64>, pub skew: f64, } impl CameraIntrinsics { /// Creates camera intrinsics that would create an identity intrinsic matrix. /// This would imply that the pixel positions have an origin at `0,0`, /// the pixel distance unit is the focal length, pixels are square, /// and there is no skew. pub fn identity() -> Self { Self { focals: Vector2::new(1.0, 1.0), skew: 0.0, principal_point: Point2::new(0.0, 0.0), } } pub fn focals(self, focals: Vector2<f64>) -> Self { Self { focals, ..self } } pub fn focal(self, focal: f64) -> Self { Self { focals: Vector2::new(focal, focal), ..self } } pub fn principal_point(self, principal_point: Point2<f64>) -> Self { Self { principal_point, ..self } } pub fn skew(self, skew: f64) -> Self { Self { skew, ..self } } #[rustfmt::skip] pub fn matrix(&self) -> Matrix3<f64> { Matrix3::new( self.focals.x, self.skew, self.principal_point.x, 0.0, self.focals.y, self.principal_point.y, 0.0, 0.0, 1.0, ) } } impl CameraModel for CameraIntrinsics { type Projection = NormalizedKeyPoint; /// Takes in a point from an image in pixel coordinates and /// converts it to a [`NormalizedKeyPoint`]. /// /// ``` /// use cv_core::{KeyPoint, CameraModel}; /// use cv_pinhole::{NormalizedKeyPoint, CameraIntrinsics}; /// use cv_core::nalgebra::{Vector2, Vector3, Point2}; /// let intrinsics = CameraIntrinsics { /// focals: Vector2::new(800.0, 900.0), /// principal_point: Point2::new(500.0, 600.0), /// skew: 1.7, /// }; /// let kp = KeyPoint(Point2::new(471.0, 322.0)); /// let nkp = intrinsics.calibrate(kp); /// let calibration_matrix = intrinsics.matrix(); /// let distance = (kp.to_homogeneous() - calibration_matrix * nkp.to_homogeneous()).norm(); /// assert!(distance < 0.1); /// ``` fn calibrate<P>(&self, point: P) -> NormalizedKeyPoint where P: ImagePoint, { let centered = point.image_point() - self.principal_point; let y = centered.y / self.focals.y; let x = (centered.x - self.skew * y) / self.focals.x; NormalizedKeyPoint(Point2::new(x, y)) } /// Converts a [`NormalizedKeyPoint`] back into pixel coordinates. /// /// ``` /// use cv_core::{KeyPoint, CameraModel}; /// use cv_pinhole::{NormalizedKeyPoint, CameraIntrinsics}; /// use cv_core::nalgebra::{Vector2, Vector3, Point2}; /// let intrinsics = CameraIntrinsics { /// focals: Vector2::new(800.0, 900.0), /// principal_point: Point2::new(500.0, 600.0), /// skew: 1.7, /// }; /// let kp = KeyPoint(Point2::new(471.0, 322.0)); /// let nkp = intrinsics.calibrate(kp); /// let ukp = intrinsics.uncalibrate(nkp); /// assert!((kp.0 - ukp.0).norm() < 1e-6); /// ``` fn uncalibrate(&self, projection: NormalizedKeyPoint) -> KeyPoint { let y = projection.y * self.focals.y; let x = projection.x * self.focals.x + self.skew * projection.y; let centered = Point2::new(x, y); KeyPoint(centered + self.principal_point.coords) } } /// This contains intrinsic camera parameters as per /// [this Wikipedia page](https://en.wikipedia.org/wiki/Camera_resectioning#Intrinsic_parameters). /// /// This also performs undistortion by applying one radial distortion coefficient (K1). #[derive(Debug, Clone, Copy, PartialEq, PartialOrd)] pub struct CameraIntrinsicsK1Distortion { pub simple_intrinsics: CameraIntrinsics, pub k1: f64, } impl CameraIntrinsicsK1Distortion { /// Creates the camera intrinsics using simple intrinsics with no distortion and a K1 distortion coefficient. pub fn new(simple_intrinsics: CameraIntrinsics, k1: f64) -> Self { Self { simple_intrinsics, k1, } } } impl CameraModel for CameraIntrinsicsK1Distortion { type Projection = NormalizedKeyPoint; /// Takes in a point from an image in pixel coordinates and /// converts it to a [`NormalizedKeyPoint`]. /// /// ``` /// use cv_core::{KeyPoint, CameraModel}; /// use cv_pinhole::{NormalizedKeyPoint, CameraIntrinsics, CameraIntrinsicsK1Distortion}; /// use cv_core::nalgebra::{Vector2, Vector3, Point2}; /// let intrinsics = CameraIntrinsics { /// focals: Vector2::new(800.0, 900.0), /// principal_point: Point2::new(500.0, 600.0), /// skew: 1.7, /// }; /// let k1 = -0.164624; /// let intrinsics = CameraIntrinsicsK1Distortion::new( /// intrinsics, /// k1, /// ); /// let kp = KeyPoint(Point2::new(471.0, 322.0)); /// let nkp = intrinsics.calibrate(kp); /// let simple_nkp = intrinsics.simple_intrinsics.calibrate(kp); /// let distance = (nkp.0.coords - (simple_nkp.0.coords / (1.0 + k1 * simple_nkp.0.coords.norm_squared()))).norm(); /// assert!(distance < 0.1); /// ``` fn calibrate<P>(&self, point: P) -> NormalizedKeyPoint where P: ImagePoint, { let NormalizedKeyPoint(distorted) = self.simple_intrinsics.calibrate(point); let r2 = distorted.coords.norm_squared(); let undistorted = (distorted.coords / (1.0 + self.k1 * r2)).into(); NormalizedKeyPoint(undistorted) } /// Converts a [`NormalizedKeyPoint`] back into pixel coordinates. /// /// ``` /// use cv_core::{KeyPoint, CameraModel}; /// use cv_pinhole::{NormalizedKeyPoint, CameraIntrinsics, CameraIntrinsicsK1Distortion}; /// use cv_core::nalgebra::{Vector2, Vector3, Point2}; /// let intrinsics = CameraIntrinsics { /// focals: Vector2::new(800.0, 900.0), /// principal_point: Point2::new(500.0, 600.0), /// skew: 1.7, /// }; /// let intrinsics = CameraIntrinsicsK1Distortion::new( /// intrinsics, /// -0.164624, /// ); /// let kp = KeyPoint(Point2::new(471.0, 322.0)); /// let nkp = intrinsics.calibrate(kp); /// let ukp = intrinsics.uncalibrate(nkp); /// assert!((kp.0 - ukp.0).norm() < 1e-6, "{:?}", (kp.0 - ukp.0).norm()); /// ``` fn uncalibrate(&self, projection: NormalizedKeyPoint) -> KeyPoint { let NormalizedKeyPoint(undistorted) = projection; // This was not easy to compute, but you can set up a quadratic to solve // for r^2 with the undistorted keypoint. This is the result. let u2 = undistorted.coords.norm_squared(); // This is actually r^2 * k1. let r2_mul_k1 = -(2.0 * self.k1 * u2 + Float::sqrt(1.0 - 4.0 * self.k1 * u2) - 1.0) / (2.0 * self.k1 * u2); self.simple_intrinsics.uncalibrate(NormalizedKeyPoint( (undistorted.coords * (1.0 + r2_mul_k1)).into(), )) } } /// This contains basic camera specifications that one could find on a /// manufacturer's website. This only contains parameters that cannot /// be changed about a camera. The focal length is not included since /// that can typically be changed and images can also be magnified. /// /// All distance units should be in meters to avoid conversion issues. #[derive(Debug, Clone, Copy, PartialEq, PartialOrd)] pub struct CameraSpecification { pub pixels: Vector2<usize>, pub pixel_dimensions: Vector2<f64>, } impl CameraSpecification { /// Creates a [`CameraSpecification`] using the sensor dimensions. pub fn from_sensor(pixels: Vector2<usize>, sensor_dimensions: Vector2<f64>) -> Self { Self { pixels, pixel_dimensions: Vector2::new( sensor_dimensions.x / pixels.x as f64, sensor_dimensions.y / pixels.y as f64, ), } } /// Creates a [`CameraSpecification`] using the sensor width assuming a square pixel. pub fn from_sensor_square(pixels: Vector2<usize>, sensor_width: f64) -> Self { let pixel_width = sensor_width / pixels.x as f64; Self { pixels, pixel_dimensions: Vector2::new(pixel_width, pixel_width), } } /// Combines the [`CameraSpecification`] with a focal length to create a [`CameraIntrinsics`]. /// /// This assumes square pixels and a perfectly centered principal point. pub fn intrinsics_centered(&self, focal: f64) -> CameraIntrinsics { CameraIntrinsics::identity() .focal(focal) .principal_point(self.pixel_dimensions.map(|p| p as f64 / 2.0 - 0.5).into()) } } /// Find the reprojection error in focal lengths of a feature match and a relative pose using the given triangulator. /// /// If the feature match destructures as `FeatureMatch(a, b)`, then A is the camera of `a`, and B is the camera of `b`. /// The pose must transform the space of camera A into camera B. The triangulator will triangulate the 3d point from the /// perspective of camera A, and the pose will be used to transform the point into the perspective of camera B. /// /// ``` /// use cv_core::{CameraToCamera, CameraPoint, FeatureMatch, Pose}; /// use cv_core::nalgebra::{Point3, IsometryMatrix3, Vector3, Rotation3}; /// use cv_pinhole::NormalizedKeyPoint; /// // Create an arbitrary point in the space of camera A. /// let point_a = CameraPoint(Point3::new(0.4, -0.25, 5.0).to_homogeneous()); /// // Create an arbitrary relative pose between two cameras A and B. /// let pose = CameraToCamera::from_parts(Vector3::new(0.1, 0.2, -0.5), Rotation3::identity()); /// // Transform the point in camera A to camera B. /// let point_b = pose.transform(point_a); /// /// // Convert the camera points to normalized image coordinates. /// let nkpa = NormalizedKeyPoint::from_camera_point(point_a).unwrap(); /// let nkpb = NormalizedKeyPoint::from_camera_point(point_b).unwrap(); /// /// // Create a triangulator. /// let triangulator = cv_geom::MinSquaresTriangulator::new(); /// /// // Since the normalized keypoints were computed exactly, there should be no reprojection error. /// let errors = cv_pinhole::pose_reprojection_error(pose, FeatureMatch(nkpa, nkpb), triangulator).unwrap(); /// let average_error = errors.iter().map(|v| v.norm()).sum::<f64>() * 0.5; /// assert!(average_error < 1e-6); /// ``` pub fn pose_reprojection_error( pose: CameraToCamera, m: FeatureMatch<NormalizedKeyPoint>, triangulator: impl TriangulatorRelative, ) -> Option<[Vector2<f64>; 2]> { let FeatureMatch(a, b) = m; triangulator .triangulate_relative(pose, a, b) .and_then(|point_a| { let reproject_a = NormalizedKeyPoint::from_camera_point(point_a)?; let point_b = pose.transform(point_a); let reproject_b = NormalizedKeyPoint::from_camera_point(point_b)?; Some([a.0 - reproject_a.0, b.0 - reproject_b.0]) }) } /// See [`pose_reprojection_error`]. /// /// This is a convenience function that simply finds the average reprojection error rather than all components. /// /// ``` /// use cv_core::{CameraToCamera, CameraPoint, FeatureMatch, Pose}; /// use cv_core::nalgebra::{Point3, IsometryMatrix3, Vector3, Rotation3}; /// use cv_pinhole::NormalizedKeyPoint; /// // Create an arbitrary point in the space of camera A. /// let point_a = CameraPoint(Point3::new(0.4, -0.25, 5.0).to_homogeneous()); /// // Create an arbitrary relative pose between two cameras A and B. /// let pose = CameraToCamera::from_parts(Vector3::new(0.1, 0.2, -0.5), Rotation3::identity()); /// // Transform the point in camera A to camera B. /// let point_b = pose.transform(point_a); /// /// // Convert the camera points to normalized image coordinates. /// let nkpa = NormalizedKeyPoint::from_camera_point(point_a).unwrap(); /// let nkpb = NormalizedKeyPoint::from_camera_point(point_b).unwrap(); /// /// // Create a triangulator. /// let triangulator = cv_geom::MinSquaresTriangulator::new(); /// /// // Since the normalized keypoints were computed exactly, there should be no reprojection error. /// let average_error = cv_pinhole::average_pose_reprojection_error(pose, FeatureMatch(nkpa, nkpb), triangulator).unwrap(); /// assert!(average_error < 1e-6); /// ``` pub fn average_pose_reprojection_error( pose: CameraToCamera, m: FeatureMatch<NormalizedKeyPoint>, triangulator: impl TriangulatorRelative, ) -> Option<f64> { pose_reprojection_error(pose, m, triangulator) .map(|errors| errors.iter().map(|v| v.norm()).sum::<f64>() * 0.5) }