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cam_poses.go
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/
cam_poses.go
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package transform
import (
"errors"
"github.com/golang/geo/r2"
"github.com/golang/geo/r3"
"gonum.org/v1/gonum/mat"
"go.viam.com/rdk/spatialmath"
)
// CamPose stores the 3x4 pose matrix as well as the 3D Rotation and Translation matrices.
type CamPose struct {
PoseMat *mat.Dense
Rotation *mat.Dense
Translation *mat.Dense
}
// NewCamPoseFromMat creates a pointer to a Camera pose from a 4x3 pose dense matrix.
func NewCamPoseFromMat(pose *mat.Dense) *CamPose {
U3 := pose.ColView(3)
t := mat.NewDense(3, 1, []float64{U3.AtVec(0), U3.AtVec(1), U3.AtVec(2)})
rot := mat.NewDense(3, 3, nil)
for i := 0; i < 3; i++ {
for j := 0; j < 3; j++ {
rot.Set(i, j, pose.At(i, j))
}
}
return &CamPose{
PoseMat: pose,
Rotation: rot,
Translation: t,
}
}
// Pose creates a spatialmath.Pose from a CamPose.
func (cp *CamPose) Pose() (spatialmath.Pose, error) {
translation := r3.Vector{cp.Translation.At(0, 0), cp.Translation.At(1, 0), cp.Translation.At(2, 0)}
rotation, err := spatialmath.NewRotationMatrix(cp.Rotation.RawMatrix().Data)
if err != nil {
return nil, err
}
return spatialmath.NewPose(translation, rotation), err
}
// adjustPoseSign adjusts the sign of a pose.
func adjustPoseSign(pose *mat.Dense) *mat.Dense {
// take 3x3 sub-matrix
subPose := pose.Slice(0, 3, 0, 3)
// if determinant is negative, scale by -1
if m := mat.DenseCopyOf(subPose); mat.Det(m) < 0 {
pose.Scale(-1, pose)
}
return pose
}
// GetPossibleCameraPoses computes all 4 possible poses from the essential matrix.
func GetPossibleCameraPoses(essMat *mat.Dense) ([]*mat.Dense, error) {
R1, R2, t, err := DecomposeEssentialMatrix(essMat)
if err != nil {
return nil, err
}
// svd
var svd mat.SVD
ok := svd.Factorize(essMat, mat.SVDFull)
if !ok {
err = errors.New("failed to factorize A")
return nil, err
}
// poses
var tOpp mat.Dense
tOpp.Scale(-1, t)
poses := make([]mat.Dense, 4)
poses[0].Augment(R1, t)
poses[1].Augment(R1, &tOpp)
poses[2].Augment(R2, t)
poses[3].Augment(R2, &tOpp)
// adjust sign of poses
posesOut := make([]*mat.Dense, 4)
for i, pose := range poses {
posesOut[i] = mat.DenseCopyOf(adjustPoseSign(&pose))
}
return posesOut, nil
}
// getCrossProductMatFromPoint returns the cross product with point p matrix.
func getCrossProductMatFromPoint(p r3.Vector) *mat.Dense {
cross := mat.NewDense(3, 3, nil)
cross.Set(0, 1, -p.Z)
cross.Set(0, 2, p.Y)
cross.Set(1, 0, p.Z)
cross.Set(1, 2, -p.X)
cross.Set(2, 0, -p.Y)
cross.Set(2, 1, p.X)
return cross
}
// GetLinearTriangulatedPoints computes triangulated 3D points with linear method.
func GetLinearTriangulatedPoints(pose *mat.Dense, pts1, pts2 []r3.Vector) ([]r3.Vector, error) {
// set identity pose for pts1
P := mat.NewDense(3, 4, nil)
P.Set(0, 0, 1)
P.Set(1, 1, 1)
P.Set(2, 2, 1)
// copy pose for pts2
Pdash := mat.DenseCopyOf(pose)
// initialize 3D points
nPoints := len(pts1)
pts3d := make([]r3.Vector, nPoints)
for i := range pts1 {
p1 := pts1[i]
p2 := pts2[i]
p1Cross := getCrossProductMatFromPoint(p1)
p2Cross := getCrossProductMatFromPoint(p2)
p1CrossP := mat.NewDense(3, 4, nil)
p1CrossP.Mul(p1Cross, P)
p2CrossPdash := mat.NewDense(3, 4, nil)
p2CrossPdash.Mul(p2Cross, Pdash)
var A mat.Dense
A.Stack(p1CrossP, p2CrossPdash)
// svd
var svd mat.SVD
ok := svd.Factorize(&A, mat.SVDFull)
if !ok {
err := errors.New("failed to factorize A")
return nil, err
}
// Determine the rank of the A matrix with a near zero condition threshold.
const rcond = 1e-15
rank := svd.Rank(rcond)
if rank == 0 {
err := errors.New("zero rank system")
return nil, err
}
var V mat.Dense
svd.VTo(&V)
pt3d := V.ColView(2)
pts3d[i] = r3.Vector{
X: pt3d.At(0, 0) / pt3d.At(3, 0),
Y: pt3d.At(1, 0) / pt3d.At(3, 0),
Z: pt3d.At(2, 0) / pt3d.At(3, 0),
}
}
return pts3d, nil
}
// GetNumberPositiveDepth computes the number of positive zs in triangulated points pts1 and pts2.
func GetNumberPositiveDepth(pose *mat.Dense, pts1, pts2 []r3.Vector, useNonLinear bool) (int, *mat.Dense) {
// get vectors from pose that are necessary to check if depth is positive
rot3 := r3.Vector{pose.At(2, 0), pose.At(2, 1), pose.At(2, 2)}
c := r3.Vector{pose.At(0, 3), pose.At(1, 3), pose.At(2, 3)}
// triangulated points
pts3D, err := GetLinearTriangulatedPoints(pose, pts1, pts2)
if err != nil {
return 0, nil
}
// Non linear triangulation can be done here to get better approximation of the 3D point
// points_3D = get_nonlinear_triangulated_points(points_3D, pose, point_list1, point_list2)
// We can then have a better approximation of the pose to get R and t
// better_approx_pose = get_approx_pose_by_non_linear_pnp(points_3D, pose, point_list1, point_list2)
// get number of positive depths in 3d points wrt to camera
nPositiveDepth := 0
for _, pt := range pts3D {
if rot3.Dot(pt.Sub(c)) > 0 {
nPositiveDepth++
}
}
return nPositiveDepth, pose
}
// GetCorrectCameraPose returns the best pose, which is the pose with the most positive depth values.
func GetCorrectCameraPose(poses []*mat.Dense, pts1, pts2 []r3.Vector) *mat.Dense {
maxNumPosDepth := 0
correctPose := poses[0]
for _, pose := range poses {
nPosDepth, betterPoseApprox := GetNumberPositiveDepth(pose, pts1, pts2, false)
if nPosDepth > maxNumPosDepth {
maxNumPosDepth = nPosDepth
correctPose = mat.DenseCopyOf(betterPoseApprox)
}
}
return correctPose
}
// EstimateNewPose estimates the pose of the camera in the second set of points wrt the pose of the camera in the first
// set of points
// pts1 and pts2 are matches in 2 images (successive in time or from 2 different cameras of the same scene
// at the same time).
func EstimateNewPose(pts1, pts2 []r2.Point, k *mat.Dense) (*CamPose, error) {
if len(pts1) != len(pts2) {
return nil, errors.New("the 2 sets of points don't have the same number of elements")
}
fundamentalMatrix, err := ComputeFundamentalMatrixAllPoints(pts1, pts2, true)
if err != nil {
return nil, err
}
essentialMatrix, err := GetEssentialMatrixFromFundamental(k, k, fundamentalMatrix)
if err != nil {
return nil, err
}
poses, err := GetPossibleCameraPoses(essentialMatrix)
if err != nil {
return nil, err
}
pts1H := Convert2DPointsToHomogeneousPoints(pts1)
pts2H := Convert2DPointsToHomogeneousPoints(pts2)
pose := GetCorrectCameraPose(poses, pts1H, pts2H)
return NewCamPoseFromMat(pose), nil
}