xform.h File Reference

Functions for computing transforms from image feature correspondences. More...

#include <cxcore.h>

Data Structures

struct  ransac_data
 holds feature data relevant to ransac More...

Defines

#define RANSAC_INLIER_FRAC_EST   0.25
 pessimistic estimate of fraction of inlers for RANSAC
#define RANSAC_PROB_BAD_SUPP   0.10
 estimate of the probability that a correspondence supports a bad model

Typedefs

typedef CvMat *(* ransac_xform_fn )(CvPoint2D64f *pts, CvPoint2D64f *mpts, int n)
 Prototype for transformation functions passed to ransac_xform().
typedef double(* ransac_err_fn )(CvPoint2D64f pt, CvPoint2D64f mpt, CvMat *T)
 Prototype for error functions passed to ransac_xform().

Functions

CvMat * ransac_xform (struct feature *features, int n, int mtype, ransac_xform_fn xform_fn, int m, double p_badxform, ransac_err_fn err_fn, double err_tol, struct feature ***inliers, int *n_in)
 Calculates a best-fit image transform from image feature correspondences using RANSAC.
CvMat * dlt_homog (CvPoint2D64f *pts, CvPoint2D64f *mpts, int n)
 Calculates a planar homography from point correspondeces using the direct linear transform.
CvMat * lsq_homog (CvPoint2D64f *pts, CvPoint2D64f *mpts, int n)
 Calculates a least-squares planar homography from point correspondeces.
double homog_xfer_err (CvPoint2D64f pt, CvPoint2D64f mpt, CvMat *H)
 Calculates the transfer error between a point and its correspondence for a given homography, i.e.
CvPoint2D64f persp_xform_pt (CvPoint2D64f pt, CvMat *T)
 Performs a perspective transformation on a single point.

Detailed Description

Functions for computing transforms from image feature correspondences.

Copyright (C) 2006-2010 Rob Hess <hess@eecs.oregonstate.edu>

Version:
1.1.2-20100521

Typedef Documentation

typedef CvMat*(* ransac_xform_fn)(CvPoint2D64f *pts, CvPoint2D64f *mpts, int n)

Prototype for transformation functions passed to ransac_xform().

Functions of this type should compute a transformation matrix given a set of point correspondences.

Parameters:
pts array of points
mpts array of corresponding points; each pts[i], i=0..n-1, corresponds to mpts[i]
n number of points in both pts and mpts
Returns:
Should return a transformation matrix that transforms each point in pts to the corresponding point in mpts or NULL on failure.
typedef double(* ransac_err_fn)(CvPoint2D64f pt, CvPoint2D64f mpt, CvMat *T)

Prototype for error functions passed to ransac_xform().

For a given point, its correspondence, and a transform, functions of this type should compute a measure of error between the correspondence and the point after the point has been transformed by the transform.

Parameters:
pt a point
mpt pt's correspondence
T a transform
Returns:
Should return a measure of error between mpt and pt after pt has been transformed by the transform T.

Function Documentation

CvMat* ransac_xform ( struct feature features,
int  n,
int  mtype,
ransac_xform_fn  xform_fn,
int  m,
double  p_badxform,
ransac_err_fn  err_fn,
double  err_tol,
struct feature ***  inliers,
int *  n_in 
)

Calculates a best-fit image transform from image feature correspondences using RANSAC.

For more information refer to:

Fischler, M. A. and Bolles, R. C. Random sample consensus: a paradigm for model fitting with applications to image analysis and automated cartography. Communications of the ACM, 24, 6 (1981), pp. 381--395.

Parameters:
features an array of features; only features with a non-NULL match of type mtype are used in homography computation
n number of features in feat
mtype determines which of each feature's match fields to use for transform computation; should be one of FEATURE_FWD_MATCH, FEATURE_BCK_MATCH, or FEATURE_MDL_MATCH; if this is FEATURE_MDL_MATCH, correspondences are assumed to be between a feature's img_pt field and its match's mdl_pt field, otherwise correspondences are assumed to be between the the feature's img_pt field and its match's img_pt field
xform_fn pointer to the function used to compute the desired transformation from feature correspondences
m minimum number of correspondences necessary to instantiate the transform computed by xform_fn
p_badxform desired probability that the final transformation returned by RANSAC is corrupted by outliers (i.e. the probability that no samples of all inliers were drawn)
err_fn pointer to the function used to compute a measure of error between putative correspondences and for a given transform
err_tol correspondences within this distance of each other are considered as inliers for a given transform
inliers if not NULL, output as an array of pointers to the final set of inliers; memory for this array is allocated by this function and must be freed by the caller using free(*inliers)
n_in if not NULL, output as the final number of inliers
Returns:
Returns a transformation matrix computed using RANSAC or NULL on error or if an acceptable transform could not be computed.
CvMat* dlt_homog ( CvPoint2D64f *  pts,
CvPoint2D64f *  mpts,
int  n 
)

Calculates a planar homography from point correspondeces using the direct linear transform.

Intended for use as a ransac_xform_fn.

Parameters:
pts array of points
mpts array of corresponding points; each pts[i], i=0..n-1, corresponds to mpts[i]
n number of points in both pts and mpts; must be at least 4
Returns:
Returns the $3 \times 3$ planar homography matrix that transforms points in pts to their corresponding points in mpts or NULL if fewer than 4 correspondences were provided
CvMat* lsq_homog ( CvPoint2D64f *  pts,
CvPoint2D64f *  mpts,
int  n 
)

Calculates a least-squares planar homography from point correspondeces.

Intended for use as a ransac_xform_fn.

Parameters:
pts array of points
mpts array of corresponding points; each pts[i], i=0..n-1, corresponds to mpts[i]
n number of points in both pts and mpts; must be at least 4
Returns:
Returns the $3 \times 3$ least-squares planar homography matrix that transforms points in pts to their corresponding points in mpts or NULL if fewer than 4 correspondences were provided
double homog_xfer_err ( CvPoint2D64f  pt,
CvPoint2D64f  mpt,
CvMat *  H 
)

Calculates the transfer error between a point and its correspondence for a given homography, i.e.

for a point $x$, it's correspondence $x'$, and homography $H$, computes $d(x', Hx)^2$. Intended for use as a ransac_err_fn.

Parameters:
pt a point
mpt pt's correspondence
H a homography matrix
Returns:
Returns the transfer error between pt and mpt given H
CvPoint2D64f persp_xform_pt ( CvPoint2D64f  pt,
CvMat *  T 
)

Performs a perspective transformation on a single point.

That is, for a point $(x, y)$ and a $3 \times 3$ matrix $T$ this function returns the point $(u, v)$, where

$[x' \ y' \ w']^T = T \times [x \ y \ 1]^T$,

and

$(u, v) = (x'/w', y'/w')$.

Note that affine transforms are a subset of perspective transforms.

Parameters:
pt a 2D point
T a perspective transformation matrix
Returns:
Returns the point $(u, v)$ as above.

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