java.lang.Object

boofcv.alg.geo.PerspectiveOps

public class PerspectiveOps extends Object

Functions related to perspective geometry and intrinsic camera calibration.

Constructor Summary

Constructors

Constructor

Description

PerspectiveOps()
Method Summary

Modifier and Type

Method

Description

static <C extends CameraPinhole> C

adjustIntrinsic(C parameters, DMatrixRMaj adjustMatrix, C adjustedParam)

Recomputes the CameraPinholeBrown given an adjustment matrix.

static <C extends CameraPinhole> C

adjustIntrinsic(C parameters, FMatrixRMaj adjustMatrix, C adjustedParam)

Recomputes the CameraPinholeBrown given an adjustment matrix.

static CameraPinhole

approximatePinhole(Point2Transform2_F64 p2n, int width, int height)

Approximates a pinhole camera using the distoriton model

static double

computeHFov(CameraPinhole intrinsic)

static double

computeVFov(CameraPinhole intrinsic)

static Point2D_F64

convertNormToPixel(CameraModel param, double x, double y, @Nullable Point2D_F64 pixel)

Convenient function for converting from normalized image coordinates to the original image pixel coordinate.

static Point2D_F32

convertNormToPixel(CameraModel param, float x, float y, @Nullable Point2D_F32 pixel)

Convenient function for converting from normalized image coordinates to the original image pixel coordinate.

static Point2D_F64

convertNormToPixel(CameraModel param, Point2D_F64 norm, @Nullable Point2D_F64 pixel)

Convenient function for converting from normalized image coordinates to the original image pixel coordinate.

static Point2D_F64

convertNormToPixel(CameraPinhole param, double x, double y, @Nullable Point2D_F64 pixel)

static Point2D_F64

convertNormToPixel(DMatrixRMaj K, Point2D_F64 norm, @Nullable Point2D_F64 pixel)

Convenient function for converting from normalized image coordinates to the original image pixel coordinate.

static Point2D_F32

convertPixelToNorm(CameraModel param, Point2D_F32 pixel, @Nullable Point2D_F32 norm)

Convenient function for converting from distorted image pixel coordinate to undistorted normalized image coordinates.

static Point2D_F64

convertPixelToNorm(CameraModel param, Point2D_F64 pixel, @Nullable Point2D_F64 norm)

Convenient function for converting from distorted image pixel coordinate to undistorted normalized image coordinates.

static Point2D_F64

convertPixelToNorm(CameraPinhole intrinsic, double x, double y, @Nullable Point2D_F64 norm)

static Point2D_F64

convertPixelToNorm(DMatrixRMaj K, Point2D_F64 pixel, @Nullable Point2D_F64 norm)

Convenient function for converting from original image pixel coordinate to normalized< image coordinates.

static Point2D_F32

convertPixelToNorm(FMatrixRMaj K, Point2D_F32 pixel, @Nullable Point2D_F32 norm)

Convenient function for converting from original image pixel coordinate to normalized< image coordinates.

static DMatrixRMaj

convertToMatrix(Se3_F64 m, DMatrixRMaj A)

Converts the SE3 into a 3x4 matrix.

static DMatrixRMaj

createCameraMatrix(DMatrixRMaj R, Vector3D_F64 T, @Nullable DMatrixRMaj K, @Nullable DMatrixRMaj ret)

Create a 3x4 camera matrix.

static CameraPinhole

createIntrinsic(int width, int height, double hfov, double vfov, @Nullable CameraPinhole intrinsic)

Creates a set of intrinsic parameters, without distortion, for a camera with the specified characteristics

static CameraPinholeBrown

createIntrinsic(int width, int height, double hfov, @Nullable CameraPinholeBrown intrinsic)

Creates a set of intrinsic parameters, without distortion, for a camera with the specified characteristics.

static WorldToCameraToPixel

createWorldToPixel(LensDistortionNarrowFOV distortion, Se3_F64 worldToCamera)

Creates a transform from world coordinates into pixel coordinates.

static WorldToCameraToPixel

createWorldToPixel(CameraPinholeBrown intrinsic, Se3_F64 worldToCamera)

Creates a transform from world coordinates into pixel coordinates.

static double

distance(Point4D_F64 a, Point4D_F64 b)

Returns a distance measure between two 3D homogenous points.

static double

distance3DvsH(Point3D_F64 a, Point4D_F64 b, double tol)

Returns the Euclidean distance between a 3D point a point homogenous coordinates.

static CameraPinhole

estimatePinhole(Point2Transform2_F64 pixelToNorm, int width, int height)

Given the transform from pixels to normalized image coordinates, create an approximate pinhole model for this camera.

static void

extractColumn(DMatrixRMaj P, int col, GeoTuple3D_F64<?> a)

Extracts a column from the camera matrix and puts it into the geometric 3-tuple.

static void

homogenousTo3dPositiveZ(Point4D_F64 p4, double farAway, double tol, Point3D_F64 p3)

Converts a 3D homogenous coordinate into a non-homogenous coordinate.

static void

inplaceAdjustCameraMatrix(double sx, double sy, double tx, double ty, DMatrixRMaj P)

Multiplies A*P, where A = [sx 0 tx; 0 sy ty; 0 0 1]

static void

insertColumn(DMatrixRMaj P, int col, GeoTuple3D_F64<?> a)

Inserts 3-tuple into the camera matrix's columns

static double

invariantAffine(Point2D_F64 p1, Point2D_F64 p2, Point2D_F64 p3, Point2D_F64 p4)

Computes an invariant under affine distortion using 4 coplanar points.

static double

invariantCrossLine(Point2D_F64 a0, Point2D_F64 a1, Point2D_F64 a2, Point2D_F64 a3)

Computes the cross-ratio between 4 points that lie along a line.

static double

invariantCrossLine(Point3D_F64 a0, Point3D_F64 a1, Point3D_F64 a2, Point3D_F64 a3)

Computes the cross-ratio between 4 points that lie along a line.

static double

invariantCrossRatio(Point2D_F64 p1, Point2D_F64 p2, Point2D_F64 p3, Point2D_F64 p4, Point2D_F64 p5)

Computes the cross-ratio (invariant for projective transform) using 5 coplanar points.

static DMatrixRMaj

invertCalibrationMatrix(DMatrixRMaj K, @Nullable DMatrixRMaj K_inv)

Inverts a camera calibration matrix using an analytic formula that takes advantage of its structure.

static void

invertPinhole(DMatrix3x3 K, DMatrix3x3 Kinv)

Analytic matrix inversion to 3x3 camera calibration matrix.

static boolean

isBehindCamera(Point4D_F64 p)

Checks to see if a point in homogenous coordinates is behind the camera, including z=0.

static <C extends CameraPinhole> C

matrixToPinhole(DMatrixRMaj K, int width, int height, C output)

Converts a calibration matrix into intrinsic parameters

static <C extends CameraPinhole> C

matrixToPinhole(FMatrixRMaj K, int width, int height, C output)

Converts a calibration matrix into intrinsic parameters

static void

multTranA(DMatrix3x3 A, DMatrix3x3 B, DMatrix3x3 C, DMatrix3x3 output)

Computes: D = A^T*B*C

static void

multTranA(DMatrixRMaj A, DMatrixRMaj B, DMatrixRMaj C, DMatrixRMaj output)

Computes: D = A^T*B*C

static void

multTranC(DMatrix3x3 A, DMatrix3x3 B, DMatrix3x3 C, DMatrix3x3 output)

Computes: D = A*B*C^T

static void

multTranC(DMatrixRMaj A, DMatrixRMaj B, DMatrixRMaj C, DMatrixRMaj output)

Computes: D = A*B*C^T

static DMatrixRMaj

pinholeToMatrix(double fx, double fy, double skew, double cx, double cy)

Given the intrinsic parameters create a calibration matrix

static void

pinholeToMatrix(double fx, double fy, double skew, double cx, double cy, DMatrix3x3 K)

static FMatrixRMaj

pinholeToMatrix(float fx, float fy, float skew, float xc, float yc)

Given the intrinsic parameters create a calibration matrix

static DMatrix3x3

pinholeToMatrix(CameraPinhole param, @Nullable DMatrix3x3 K)

Given the intrinsic parameters create a calibration matrix

static DMatrixRMaj

pinholeToMatrix(CameraPinhole param, @Nullable DMatrixRMaj K)

Given the intrinsic parameters create a calibration matrix

static FMatrixRMaj

pinholeToMatrix(CameraPinhole param, @Nullable FMatrixRMaj K)

Given the intrinsic parameters create a calibration matrix

static void

projectionCombine(DMatrixRMaj M, Vector3D_F64 T, DMatrixRMaj P)

P = [M|T]

static void

projectionSplit(DMatrixRMaj P, DMatrix3x3 M, DMatrix3 T)

Splits the projection matrix into a 3x3 matrix and 3x1 vector.

static void

projectionSplit(DMatrixRMaj P, DMatrixRMaj M, Vector3D_F64 T)

Splits the projection matrix into a 3x3 matrix and 3x1 vector.

static Point2D_F64

renderPixel(CameraPinhole intrinsic, Point3D_F64 X, @Nullable Point2D_F64 pixel)

Renders a point in camera coordinates into the image plane in pixels.

static Point2D_F64

renderPixel(CameraPinhole intrinsic, Point4D_F64 X, @Nullable Point2D_F64 pixel)

static @Nullable Point2D_F64

renderPixel(Se3_F64 worldToCamera, @Nullable DMatrixRMaj K, Point3D_F64 X, @Nullable Point2D_F64 pixel)

Renders a point in world coordinates into the image plane in pixels or normalized image coordinates.

static @Nullable Point2D_F64

renderPixel(Se3_F64 worldToCamera, CameraPinhole K, Point3D_F64 X, @Nullable Point2D_F64 pixel)

static @Nullable Point2D_F64

renderPixel(Se3_F64 worldToCamera, CameraPinhole K, Point4D_F64 X, @Nullable Point2D_F64 pixel)

static @Nullable Point2D_F64

renderPixel(Se3_F64 worldToCamera, Point3D_F64 X, @Nullable Point2D_F64 pixel)

static Point2D_F64

renderPixel(DMatrixRMaj worldToCamera, Point3D_F64 X)

Computes the image coordinate of a point given its 3D location and the camera matrix.

static Point2D_F64

renderPixel(DMatrixRMaj worldToCamera, Point3D_F64 X, @Nullable Point2D_F64 pixel)

static Point3D_F64

renderPixel(DMatrixRMaj worldToCamera, Point3D_F64 X, @Nullable Point3D_F64 pixel)

static Point2D_F64

renderPixel(DMatrixRMaj cameraMatrix, Point4D_F64 X, @Nullable Point2D_F64 x)

Render a pixel in homogeneous coordinates from a 3x4 camera matrix and a 2D point.

static Point3D_F64

renderPixel(DMatrixRMaj cameraMatrix, Point4D_F64 X, @Nullable Point3D_F64 x)

Render a pixel in homogeneous coordinates from a 3x4 camera matrix and a 3D homogeneous point.

static Point3D_F64

renderPointing(Se3_F64 worldToCamera, Point3D_F64 X, @Nullable Point3D_F64 pixel)

Renders an observations as a pointing vector.

static void

rotateH(DMatrixRMaj R, Point4D_F64 src, Point4D_F64 dst)

Applies a rotation to a homogenous 3D point

static void

rotateInvH(DMatrixRMaj R, Point4D_F64 src, Point4D_F64 dst)

Applies a rotation in reverse to a homogenous 3D point

static void

scaleIntrinsic(CameraPinhole param, double scale)

Multiplies each element of the intrinsic parameters by the provided scale factor.

static void

splitAssociated(List<AssociatedPair> pairs, List<Point2D_F64> view1, List<Point2D_F64> view2)

Takes a list of AssociatedPair as input and breaks it up into two lists for each view.

static void

splitAssociated(List<AssociatedTriple> pairs, List<Point2D_F64> view1, List<Point2D_F64> view2, List<Point2D_F64> view3)

Takes a list of AssociatedTriple as input and breaks it up into three lists for each view.

Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Details
- PerspectiveOps
  
  public PerspectiveOps()
Method Details
- approximatePinhole
  
  public static CameraPinhole approximatePinhole(Point2Transform2_F64 p2n, int width, int height)
  
  Approximates a pinhole camera using the distoriton model
  
  Parameters:
  
  p2n - Distorted pixel to undistorted normalized image coordinates
- createIntrinsic
  
  public static CameraPinhole createIntrinsic(int width, int height, double hfov, double vfov, @Nullable @Nullable CameraPinhole intrinsic)
  
  Creates a set of intrinsic parameters, without distortion, for a camera with the specified characteristics
  
  Parameters:
  
  width - Image width
  
  height - Image height
  
  hfov - Horizontal FOV in degrees. If <= 0 then it will be set to the vfov
  
  vfov - Vertical FOV in degrees. If <= 0 then it will be set to the hfov
  
  Returns:
  
  guess camera parameters
- createIntrinsic
  
  public static CameraPinholeBrown createIntrinsic(int width, int height, double hfov, @Nullable @Nullable CameraPinholeBrown intrinsic)
  
  Creates a set of intrinsic parameters, without distortion, for a camera with the specified characteristics. The focal length is assumed to be the same for x and y.
  
  Parameters:
  
  width - Image width
  
  height - Image height
  
  hfov - Horizontal FOV in degrees
  
  Returns:
  
  guess camera parameters
- scaleIntrinsic
  
  public static void scaleIntrinsic(CameraPinhole param, double scale)
  
  Multiplies each element of the intrinsic parameters by the provided scale factor. Useful if the image has been rescaled.
  
  Parameters:
  
  param - Intrinsic parameters
  
  scale - Scale factor that input image is being scaled by.
- adjustIntrinsic
  
  public static <C extends CameraPinhole> C adjustIntrinsic(C parameters, DMatrixRMaj adjustMatrix, C adjustedParam)
  
  Recomputes the CameraPinholeBrown given an adjustment matrix.
  K_A = A*K
  Where K_A is the returned adjusted intrinsic matrix, A is the adjustment matrix and K is the original intrinsic calibration matrix.
  NOTE: Distortion parameters are ignored in the provided CameraPinholeBrown class.
  
  Parameters:
  
  parameters - (Input) Original intrinsic parameters. Not modified.
  
  adjustMatrix - (Input) Adjustment matrix. Not modified.
  
  adjustedParam - (Output) Optional storage for adjusted intrinsic parameters. Can be null.
  
  Returns:
  
  Adjusted intrinsic parameters.
- adjustIntrinsic
  
  public static <C extends CameraPinhole> C adjustIntrinsic(C parameters, FMatrixRMaj adjustMatrix, C adjustedParam)
  
  Recomputes the CameraPinholeBrown given an adjustment matrix.
  K_A = A*K
  Where K_A is the returned adjusted intrinsic matrix, A is the adjustment matrix and K is the original intrinsic calibration matrix.
  NOTE: Distortion parameters are ignored in the provided CameraPinholeBrown class.
  
  Parameters:
  
  parameters - (Input) Original intrinsic parameters. Not modified.
  
  adjustMatrix - (Input) Adjustment matrix. Not modified.
  
  adjustedParam - (Output) Optional storage for adjusted intrinsic parameters. Can be null.
  
  Returns:
  
  Adjusted intrinsic parameters.
- pinholeToMatrix
  
  public static DMatrixRMaj pinholeToMatrix(double fx, double fy, double skew, double cx, double cy)
  
  Given the intrinsic parameters create a calibration matrix
  
  Parameters:
  
  fx - Focal length x-axis in pixels
  
  fy - Focal length y-axis in pixels
  
  skew - skew in pixels
  
  cx - camera center x-axis in pixels
  
  cy - center center y-axis in pixels
  
  Returns:
  
  Calibration matrix 3x3
- pinholeToMatrix
  
  public static void pinholeToMatrix(double fx, double fy, double skew, double cx, double cy, DMatrix3x3 K)
- invertPinhole
  
  public static void invertPinhole(DMatrix3x3 K, DMatrix3x3 Kinv)
  
  Analytic matrix inversion to 3x3 camera calibration matrix. Input and output can be the same matrix. Zeros are not set.
  
  Parameters:
  
  K - (Input) Calibration matrix
  
  Kinv - (Output) inverse.
- pinholeToMatrix
  
  public static FMatrixRMaj pinholeToMatrix(float fx, float fy, float skew, float xc, float yc)
  
  Given the intrinsic parameters create a calibration matrix
  
  Parameters:
  
  fx - Focal length x-axis in pixels
  
  fy - Focal length y-axis in pixels
  
  skew - skew in pixels
  
  xc - camera center x-axis in pixels
  
  yc - center center y-axis in pixels
  
  Returns:
  
  Calibration matrix 3x3
- pinholeToMatrix
  
  public static DMatrixRMaj pinholeToMatrix(CameraPinhole param, @Nullable @Nullable DMatrixRMaj K)
  
  Given the intrinsic parameters create a calibration matrix
  
  Parameters:
  
  param - Intrinsic parameters structure that is to be converted into a matrix
  
  K - Storage for calibration matrix, must be 3x3. If null then a new matrix is declared
  
  Returns:
  
  Calibration matrix 3x3
- pinholeToMatrix
  
  public static FMatrixRMaj pinholeToMatrix(CameraPinhole param, @Nullable @Nullable FMatrixRMaj K)
  
  Given the intrinsic parameters create a calibration matrix
  
  Parameters:
  
  param - Intrinsic parameters structure that is to be converted into a matrix
  
  K - Storage for calibration matrix, must be 3x3. If null then a new matrix is declared
  
  Returns:
  
  Calibration matrix 3x3
- pinholeToMatrix
  
  public static DMatrix3x3 pinholeToMatrix(CameraPinhole param, @Nullable @Nullable DMatrix3x3 K)
  
  Given the intrinsic parameters create a calibration matrix
  
  Parameters:
  
  param - Intrinsic parameters structure that is to be converted into a matrix
  
  K - Storage for calibration matrix, must be 3x3. If null then a new matrix is declared
  
  Returns:
  
  Calibration matrix 3x3
- matrixToPinhole
  
  public static <C extends CameraPinhole> C matrixToPinhole(DMatrixRMaj K, int width, int height, @Nullable C output)
  
  Converts a calibration matrix into intrinsic parameters
  
  Parameters:
  
  K - Camera calibration matrix.
  
  width - Image width in pixels
  
  height - Image height in pixels
  
  output - (Output) Where the intrinsic parameter are written to. If null then a new instance is declared.
  
  Returns:
  
  camera parameters
- matrixToPinhole
  
  public static <C extends CameraPinhole> C matrixToPinhole(FMatrixRMaj K, int width, int height, @Nullable C output)
  
  Converts a calibration matrix into intrinsic parameters
  
  Parameters:
  
  K - Camera calibration matrix.
  
  width - Image width in pixels
  
  height - Image height in pixels
  
  output - (Output) Where the intrinsic parameter are written to. If null then a new instance is declared.
  
  Returns:
  
  camera parameters
- estimatePinhole
  
  public static CameraPinhole estimatePinhole(Point2Transform2_F64 pixelToNorm, int width, int height)
  
  Given the transform from pixels to normalized image coordinates, create an approximate pinhole model for this camera. Assumes (cx,cy) is the image center and that there is no skew.
  
  Parameters:
  
  pixelToNorm - Pixel coordinates into normalized image coordinates
  
  width - Input image's width
  
  height - Input image's height
  
  Returns:
  
  Approximate pinhole camera
- convertNormToPixel
  
  public static Point2D_F64 convertNormToPixel(CameraModel param, double x, double y, @Nullable @Nullable Point2D_F64 pixel)
  
  Convenient function for converting from normalized image coordinates to the original image pixel coordinate. If speed is a concern then PinholeNtoP_F64 should be used instead.
  
  Parameters:
  
  param - Intrinsic camera parameters
  
  x - X-coordinate of normalized.
  
  y - Y-coordinate of normalized.
  
  pixel - Optional storage for output. If null a new instance will be declared.
  
  Returns:
  
  pixel image coordinate
- convertNormToPixel
  
  public static Point2D_F64 convertNormToPixel(CameraPinhole param, double x, double y, @Nullable @Nullable Point2D_F64 pixel)
- convertNormToPixel
  
  public static Point2D_F32 convertNormToPixel(CameraModel param, float x, float y, @Nullable @Nullable Point2D_F32 pixel)
  
  Convenient function for converting from normalized image coordinates to the original image pixel coordinate. If speed is a concern then PinholeNtoP_F64 should be used instead.
  
  Parameters:
  
  param - Intrinsic camera parameters
  
  x - X-coordinate of normalized.
  
  y - Y-coordinate of normalized.
  
  pixel - Optional storage for output. If null a new instance will be declared.
  
  Returns:
  
  pixel image coordinate
- convertNormToPixel
  
  public static Point2D_F64 convertNormToPixel(CameraModel param, Point2D_F64 norm, @Nullable @Nullable Point2D_F64 pixel)
  
  Convenient function for converting from normalized image coordinates to the original image pixel coordinate. If speed is a concern then PinholeNtoP_F64 should be used instead.
  NOTE: norm and pixel can be the same instance.
  
  Parameters:
  
  param - Intrinsic camera parameters
  
  norm - Normalized image coordinate.
  
  pixel - Optional storage for output. If null a new instance will be declared.
  
  Returns:
  
  pixel image coordinate
- convertNormToPixel
  
  public static Point2D_F64 convertNormToPixel(DMatrixRMaj K, Point2D_F64 norm, @Nullable @Nullable Point2D_F64 pixel)
  
  Convenient function for converting from normalized image coordinates to the original image pixel coordinate. If speed is a concern then PinholeNtoP_F64 should be used instead.
  NOTE: norm and pixel can be the same instance.
  
  Parameters:
  
  K - Intrinsic camera calibration matrix
  
  norm - Normalized image coordinate.
  
  pixel - Optional storage for output. If null a new instance will be declared.
  
  Returns:
  
  pixel image coordinate
- convertPixelToNorm
  
  public static Point2D_F64 convertPixelToNorm(CameraModel param, Point2D_F64 pixel, @Nullable @Nullable Point2D_F64 norm)
  
  Convenient function for converting from distorted image pixel coordinate to undistorted normalized image coordinates. If speed is a concern then PinholePtoN_F64 should be used instead.
  NOTE: norm and pixel can be the same instance.
  
  Parameters:
  
  param - Intrinsic camera parameters
  
  pixel - Pixel coordinate
  
  norm - Optional storage for output. If null a new instance will be declared.
  
  Returns:
  
  normalized image coordinate
- convertPixelToNorm
  
  public static Point2D_F32 convertPixelToNorm(CameraModel param, Point2D_F32 pixel, @Nullable @Nullable Point2D_F32 norm)
  
  Convenient function for converting from distorted image pixel coordinate to undistorted normalized image coordinates. If speed is a concern then PinholePtoN_F32 should be used instead.
  NOTE: norm and pixel can be the same instance.
  
  Parameters:
  
  param - Intrinsic camera parameters
  
  pixel - Pixel coordinate
  
  norm - Optional storage for output. If null a new instance will be declared.
  
  Returns:
  
  normalized image coordinate
- convertPixelToNorm
  
  public static Point2D_F64 convertPixelToNorm(DMatrixRMaj K, Point2D_F64 pixel, @Nullable @Nullable Point2D_F64 norm)
  
  Convenient function for converting from original image pixel coordinate to normalized< image coordinates. If speed is a concern then PinholePtoN_F64 should be used instead.
  NOTE: norm and pixel can be the same instance.
  
  Parameters:
  
  K - Intrinsic camera calibration matrix
  
  pixel - Pixel coordinate.
  
  norm - Optional storage for output. If null a new instance will be declared.
  
  Returns:
  
  normalized image coordinate
- convertPixelToNorm
  
  public static Point2D_F32 convertPixelToNorm(FMatrixRMaj K, Point2D_F32 pixel, @Nullable @Nullable Point2D_F32 norm)
  
  Convenient function for converting from original image pixel coordinate to normalized< image coordinates. If speed is a concern then PinholePtoN_F64 should be used instead.
  NOTE: norm and pixel can be the same instance.
  
  Parameters:
  
  K - Intrinsic camera calibration matrix
  
  pixel - Pixel coordinate.
  
  norm - Optional storage for output. If null a new instance will be declared.
  
  Returns:
  
  normalized image coordinate
- convertPixelToNorm
  
  public static Point2D_F64 convertPixelToNorm(CameraPinhole intrinsic, double x, double y, @Nullable @Nullable Point2D_F64 norm)
- renderPixel
  
  @Nullable public static @Nullable Point2D_F64 renderPixel(Se3_F64 worldToCamera, @Nullable @Nullable DMatrixRMaj K, Point3D_F64 X, @Nullable @Nullable Point2D_F64 pixel)
  
  Renders a point in world coordinates into the image plane in pixels or normalized image coordinates.
  
  Parameters:
  
  worldToCamera - Transform from world to camera frame
  
  K - Optional. Intrinsic camera calibration matrix. If null then normalized image coordinates are returned.
  
  X - 3D Point in world reference frame..
  
  pixel - (Output) storage for the rendered pixel
  
  Returns:
  
  2D Render point on image plane or null if it's behind the camera
- renderPixel
  
  @Nullable public static @Nullable Point2D_F64 renderPixel(Se3_F64 worldToCamera, CameraPinhole K, Point3D_F64 X, @Nullable @Nullable Point2D_F64 pixel)
- renderPixel
  
  @Nullable public static @Nullable Point2D_F64 renderPixel(Se3_F64 worldToCamera, CameraPinhole K, Point4D_F64 X, @Nullable @Nullable Point2D_F64 pixel)
- renderPixel
  
  @Nullable public static @Nullable Point2D_F64 renderPixel(Se3_F64 worldToCamera, Point3D_F64 X, @Nullable @Nullable Point2D_F64 pixel)
- renderPointing
  
  public static Point3D_F64 renderPointing(Se3_F64 worldToCamera, Point3D_F64 X, @Nullable @Nullable Point3D_F64 pixel)
  
  Renders an observations as a pointing vector.
  
  Parameters:
  
  X - 3D Point in world reference frame.
  
  pixel - (Output) storage for the rendered pixel
  
  Returns:
  
  Rendering observations as a pointing vector
- renderPixel
  
  public static Point2D_F64 renderPixel(CameraPinhole intrinsic, Point3D_F64 X, @Nullable @Nullable Point2D_F64 pixel)
  
  Renders a point in camera coordinates into the image plane in pixels. Does not check to see if the point is behind the camera or not
  
  Parameters:
  
  intrinsic - Intrinsic camera parameters.
  
  X - 3D Point in camera reference frame..
  
  pixel - (Output) Storage for output pixel. Can be null
  
  Returns:
  
  2D Render point on image plane
- renderPixel
  
  public static Point2D_F64 renderPixel(CameraPinhole intrinsic, Point4D_F64 X, @Nullable @Nullable Point2D_F64 pixel)
- renderPixel
  
  public static Point2D_F64 renderPixel(DMatrixRMaj worldToCamera, Point3D_F64 X)
  
  Computes the image coordinate of a point given its 3D location and the camera matrix.
  
  Parameters:
  
  worldToCamera - 3x4 camera matrix for transforming a 3D point from world to image coordinates.
  
  X - 3D Point in world reference frame..
  
  Returns:
  
  2D Render point on image plane.
- renderPixel
  
  public static Point2D_F64 renderPixel(DMatrixRMaj worldToCamera, Point3D_F64 X, @Nullable @Nullable Point2D_F64 pixel)
- renderPixel
  
  public static Point3D_F64 renderPixel(DMatrixRMaj worldToCamera, Point3D_F64 X, @Nullable @Nullable Point3D_F64 pixel)
- renderPixel
  
  public static Point3D_F64 renderPixel(DMatrixRMaj cameraMatrix, Point4D_F64 X, @Nullable @Nullable Point3D_F64 x)
  
  Render a pixel in homogeneous coordinates from a 3x4 camera matrix and a 3D homogeneous point.
  
  Parameters:
  
  cameraMatrix - (Input) 3x4 camera matrix
  
  X - (Input) 3D point in homogeneous coordinates
  
  x - (Output) Rendered 2D point in homogeneous coordinates
  
  Returns:
  
  Rendered 2D point in homogeneous coordinates
- renderPixel
  
  public static Point2D_F64 renderPixel(DMatrixRMaj cameraMatrix, Point4D_F64 X, @Nullable @Nullable Point2D_F64 x)
  
  Render a pixel in homogeneous coordinates from a 3x4 camera matrix and a 2D point.
  
  Parameters:
  
  cameraMatrix - (Input) 3x4 camera matrix
  
  X - (Input) 3D point in homogeneous coordinates
  
  x - (Output) Rendered 2D point coordinates
  
  Returns:
  
  Rendered 2D point coordinates
- splitAssociated
  
  public static void splitAssociated(List<AssociatedPair> pairs, List<Point2D_F64> view1, List<Point2D_F64> view2)
  
  Takes a list of AssociatedPair as input and breaks it up into two lists for each view.
  
  Parameters:
  
  pairs - Input: List of associated pairs.
  
  view1 - Output: List of observations from view 1
  
  view2 - Output: List of observations from view 2
- splitAssociated
  
  public static void splitAssociated(List<AssociatedTriple> pairs, List<Point2D_F64> view1, List<Point2D_F64> view2, List<Point2D_F64> view3)
  
  Takes a list of AssociatedTriple as input and breaks it up into three lists for each view.
  
  Parameters:
  
  pairs - Input: List of associated triples.
  
  view1 - Output: List of observations from view 1
  
  view2 - Output: List of observations from view 2
  
  view3 - Output: List of observations from view 3
- createCameraMatrix
  
  public static DMatrixRMaj createCameraMatrix(DMatrixRMaj R, Vector3D_F64 T, @Nullable @Nullable DMatrixRMaj K, @Nullable @Nullable DMatrixRMaj ret)
  
  Create a 3x4 camera matrix. For calibrated camera P = [R|T]. For uncalibrated camera it is P = K*[R|T].
  
  Parameters:
  
  R - Rotation matrix. 3x3
  
  T - Translation vector.
  
  K - Optional camera calibration matrix 3x3.
  
  ret - Storage for camera calibration matrix. If null a new instance will be created.
  
  Returns:
  
  Camera calibration matrix.
- projectionSplit
  
  public static void projectionSplit(DMatrixRMaj P, DMatrixRMaj M, Vector3D_F64 T)
  
  Splits the projection matrix into a 3x3 matrix and 3x1 vector.
  
  Parameters:
  
  P - (Input) 3x4 projection matrix
  
  M - (Output) M = P(:,0:2)
  
  T - (Output) T = P(:,3)
- projectionSplit
  
  public static void projectionSplit(DMatrixRMaj P, DMatrix3x3 M, DMatrix3 T)
  
  Splits the projection matrix into a 3x3 matrix and 3x1 vector.
  
  Parameters:
  
  P - (Input) 3x4 projection matirx
  
  M - (Output) M = P(:,0:2)
  
  T - (Output) T = P(:,3)
- projectionCombine
  
  public static void projectionCombine(DMatrixRMaj M, Vector3D_F64 T, DMatrixRMaj P)
  
  P = [M|T]
  
  Parameters:
  
  M - (Input) 3x3 matrix
  
  T - (Input) 3x1 vector
  
  P - (Output) [M,T]
- createWorldToPixel
  
  public static WorldToCameraToPixel createWorldToPixel(CameraPinholeBrown intrinsic, Se3_F64 worldToCamera)
  
  Creates a transform from world coordinates into pixel coordinates. can handle lens distortion
- createWorldToPixel
  
  public static WorldToCameraToPixel createWorldToPixel(LensDistortionNarrowFOV distortion, Se3_F64 worldToCamera)
  
  Creates a transform from world coordinates into pixel coordinates. can handle lens distortion
- computeHFov
  
  public static double computeHFov(CameraPinhole intrinsic)
- computeVFov
  
  public static double computeVFov(CameraPinhole intrinsic)
- convertToMatrix
  
  public static DMatrixRMaj convertToMatrix(Se3_F64 m, DMatrixRMaj A)
  
  Converts the SE3 into a 3x4 matrix. [R|T]
  
  Parameters:
  
  m - (Input) transform
  
  A - (Output) equivalent 3x4 matrix represenation
- extractColumn
  
  public static void extractColumn(DMatrixRMaj P, int col, GeoTuple3D_F64<?> a)
  
  Extracts a column from the camera matrix and puts it into the geometric 3-tuple.
- insertColumn
  
  public static void insertColumn(DMatrixRMaj P, int col, GeoTuple3D_F64<?> a)
  
  Inserts 3-tuple into the camera matrix's columns
- multTranA
  
  public static void multTranA(DMatrixRMaj A, DMatrixRMaj B, DMatrixRMaj C, DMatrixRMaj output)
  
  Computes: D = A^T*B*C
  
  Parameters:
  
  A - (Input) 3x3 matrix
  
  B - (Input) 3x3 matrix
  
  C - (Input) 3x3 matrix
  
  output - (Output) 3x3 matrix. Can be same instance A or B.
- multTranC
  
  public static void multTranC(DMatrixRMaj A, DMatrixRMaj B, DMatrixRMaj C, DMatrixRMaj output)
  
  Computes: D = A*B*C^T
  
  Parameters:
  
  A - (Input) 3x3 matrix
  
  B - (Input) 3x3 matrix
  
  C - (Input) 3x3 matrix
  
  output - (Output) 3x3 matrix. Can be same instance A or B.
- multTranA
  
  public static void multTranA(DMatrix3x3 A, DMatrix3x3 B, DMatrix3x3 C, DMatrix3x3 output)
  
  Computes: D = A^T*B*C
  
  Parameters:
  
  A - (Input) 3x3 matrix
  
  B - (Input) 3x3 matrix
  
  C - (Input) 3x3 matrix
  
  output - (Output) 3x3 matrix. Can be same instance A or B.
- multTranC
  
  public static void multTranC(DMatrix3x3 A, DMatrix3x3 B, DMatrix3x3 C, DMatrix3x3 output)
  
  Computes: D = A*B*C^T
  
  Parameters:
  
  A - (Input) 3x3 matrix
  
  B - (Input) 3x3 matrix
  
  C - (Input) 3x3 matrix
  
  output - (Output) 3x3 matrix. Can be same instance A or B.
- inplaceAdjustCameraMatrix
  
  public static void inplaceAdjustCameraMatrix(double sx, double sy, double tx, double ty, DMatrixRMaj P)
  
  Multiplies A*P, where A = [sx 0 tx; 0 sy ty; 0 0 1]
- invariantCrossLine
  
  public static double invariantCrossLine(Point3D_F64 a0, Point3D_F64 a1, Point3D_F64 a2, Point3D_F64 a3)
  
  Computes the cross-ratio between 4 points that lie along a line. This is an invariant under projective geometry.
  
  Parameters:
  
  a0 - Unique point on a line
  
  a1 - Unique point on a line
  
  a2 - Unique point on a line
  
  a3 - Unique point on a line
  
  Returns:
  
  cross ratio
- invariantCrossLine
  
  public static double invariantCrossLine(Point2D_F64 a0, Point2D_F64 a1, Point2D_F64 a2, Point2D_F64 a3)
  
  Computes the cross-ratio between 4 points that lie along a line. This is an invariant under projective geometry.
  
  Parameters:
  
  a0 - Unique point on a line
  
  a1 - Unique point on a line
  
  a2 - Unique point on a line
  
  a3 - Unique point on a line
  
  Returns:
  
  cross ratio
- invariantCrossRatio
  
  public static double invariantCrossRatio(Point2D_F64 p1, Point2D_F64 p2, Point2D_F64 p3, Point2D_F64 p4, Point2D_F64 p5)
  
  Computes the cross-ratio (invariant for projective transform) using 5 coplanar points.
  
  cross ratio = P(1,2,3)*P(1,4,5)/(P(1,2,4)*P(1,3,5))
  where P() is the area of a triangle defined by the 3 points.
  
  NOTE: Perspective and projective transforms are the same thing
  
  Nakai, Tomohiro, Koichi Kise, and Masakazu Iwamura. "Hashing with local combinations of feature points and its application to camera-based document image retrieval." Proc. CBDAR05 (2005): 87-94.
- invariantAffine
  
  public static double invariantAffine(Point2D_F64 p1, Point2D_F64 p2, Point2D_F64 p3, Point2D_F64 p4)
  
  Computes an invariant under affine distortion using 4 coplanar points.
  
  invariant = P(1,3,4)/P(1,2,3)
  where P() is the area of a triangle defined by the 3 points.
- homogenousTo3dPositiveZ
  
  public static void homogenousTo3dPositiveZ(Point4D_F64 p4, double farAway, double tol, Point3D_F64 p3)
  
  Converts a 3D homogenous coordinate into a non-homogenous coordinate. Things get tricky when a point is at or "close to" infinity. This situation is handled by throwing it at some distant location. This is a reasonable approach when you can't just skip the point. It's assumed that points at infinity have a positive Z value.
  
  Parameters:
  
  p4 - (Input) Homogenous coordinate.
  
  farAway - (Input) How far away points at infinity should be put. Application dependent. Try 1e9
  
  tol - (Input) Tolerance for defining a point at infinity. If p4 has a norm of 1 then 1e-7 is probably reasonable.
  
  p3 - (output) Cartesian coordinate.
- distance
  
  public static double distance(Point4D_F64 a, Point4D_F64 b)
  
  Returns a distance measure between two 3D homogenous points. There is no well defined way to measure distance in homogenous space.
  distance = norm( a/norm(a) - b/norm(b) )
  
  Parameters:
  
  a - 3D homogneous point
  
  b - 3D homogneous point
  
  Returns:
  
  A distance measure
- distance3DvsH
  
  public static double distance3DvsH(Point3D_F64 a, Point4D_F64 b, double tol)
  
  Returns the Euclidean distance between a 3D point a point homogenous coordinates. If the homogenous point is at infinity, within tolererance, then Double.POSITIVE_INFINITY is returned.
  
  Parameters:
  
  a - (Input) 3D point
  
  b - (Input) Homogenous point
  
  tol - (Input) Tolerance for point being at infinity. Closer to zero means more strict. Try 1e-8
  
  Returns:
  
  Euclidean distance
- isBehindCamera
  
  public static boolean isBehindCamera(Point4D_F64 p)
  
  Checks to see if a point in homogenous coordinates is behind the camera, including z=0. This is made more complex as the possibility that it's at infinity needs to be explicitly checked and handled.
  
  if a point lies on the (x-y) plane exactly it will be considered behind the camera.
  
  Returns:
  
  true if it's behind the camera (z < 0.0)
- invertCalibrationMatrix
  
  public static DMatrixRMaj invertCalibrationMatrix(DMatrixRMaj K, @Nullable @Nullable DMatrixRMaj K_inv)
  
  Inverts a camera calibration matrix using an analytic formula that takes advantage of its structure. K and K_inv can be the same instance.
  
  Parameters:
  
  K - (Input) 3x3 intrinsic calibration matrix
  
  K_inv - (Output) inverted calibration matrix.
- rotateH
  
  public static void rotateH(DMatrixRMaj R, Point4D_F64 src, Point4D_F64 dst)
  
  Applies a rotation to a homogenous 3D point
  
  Parameters:
  
  R - rotation matrix.
  
  src - (Input) point
  
  dst - (Output) point. Can be same instance as src
- rotateInvH
  
  public static void rotateInvH(DMatrixRMaj R, Point4D_F64 src, Point4D_F64 dst)
  
  Applies a rotation in reverse to a homogenous 3D point
  
  Parameters:
  
  R - rotation matrix.
  
  src - (Input) point
  
  dst - (Output) point. Can be same instance as src

Class PerspectiveOps

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Constructor Details

PerspectiveOps

Method Details

approximatePinhole

createIntrinsic

createIntrinsic

scaleIntrinsic

adjustIntrinsic

adjustIntrinsic

pinholeToMatrix

pinholeToMatrix

invertPinhole

pinholeToMatrix

pinholeToMatrix

pinholeToMatrix

pinholeToMatrix

matrixToPinhole

matrixToPinhole

estimatePinhole

convertNormToPixel

convertNormToPixel

convertNormToPixel

convertNormToPixel

convertNormToPixel

convertPixelToNorm

convertPixelToNorm

convertPixelToNorm

convertPixelToNorm

convertPixelToNorm

renderPixel

renderPixel

renderPixel

renderPixel

renderPointing

renderPixel

renderPixel

renderPixel

renderPixel

renderPixel

renderPixel

renderPixel

splitAssociated

splitAssociated

createCameraMatrix

projectionSplit

projectionSplit

projectionCombine

createWorldToPixel

createWorldToPixel

computeHFov

computeVFov

convertToMatrix

extractColumn

insertColumn

multTranA

multTranC

multTranA

multTranC

inplaceAdjustCameraMatrix

invariantCrossLine

invariantCrossLine

invariantCrossRatio

invariantAffine

homogenousTo3dPositiveZ

distance

distance3DvsH

isBehindCamera

invertCalibrationMatrix

rotateH

rotateInvH