School of Computer Science & Software Engineering
The University of Western Australia
Crawley, Western Autralia. 6009
Note I am no longer employed by UWA though I maintain an association with
UWA via an unpaid adjunct appointment. I am not in a position to take
on new graduate students or offer internships.
Please report any bugs and/or suggest enhancements to
I receive so many mail messages regarding this
site that I have difficulty responding to them all.
I will endeavor to respond to mail
that directly concerns the use of individual functions.
However, please note I do not have the time to provide an on-line vision
problem solving service!
Cheers,
Peter Kovesi
The complete set of these functions is available as a gzipped tar file
MatlabFns.tar.gz for Unix users.
Once you have untarred this file MATLAB users should remove the Octave
subdirectory from this package (or ensure it is not in your MATLAB
path) to avoid problems.
phasecong.m Code for
calculating phase congruency in an image. Phase congruency is an
illumination and contrast invariant measure of feature
significance. It also correctly detects features at all kind of
phase angle, and not just step features with a phase angle of 0 or 180
degrees. This function also returns a feature type image. Note
however, this function is now only here for reference reasons, I now
recommend that you use phasecong2 below.
phasecong2.m New phase
congruency code that combines edge and corner detection, and provides
better localization. This function supersedes phasecong.m above.
dispfeat.m This
function provides visualisation and statistics of the different
feature types found in an image by phasecong. Typically you will find
a broad distribution of all feature types between step edges and
lines. This function needs edgelink.m (see below).
odot.m Demonstrates
the actions of the 'Odot' and 'Oslash' operators on a 1D signal.
These operators allow one to decompose and combine signals in a way
that is consistent with the Local Energy model of feature perception.
spatialgabor.m applies
a single oriented Gabor filter to an image.
phase symmetry image
phasesym.m Code for
calculating phase symmetry. This can be used as a line and blob
detector. Phase symmetry is an illumination and contrast invariant
measure of symmetry in an image. (A bright circle is not more
'symmetric' than a grey circle as can be the case with some other
measures!).
gaborconvolve.m Code for
convolving an image with a bank of log-Gabor filters. A
pre-processing step for texture analysis, feature detection and
classification, etc.
plotgaborfilters.m A
function for plotting log-Gabor filters. This function is useful for
seeing what effect the various parameter settings have on the
formation of a log-Gabor filter bankused in the functions above.
monofilt.m An
implementation of Felsberg's monogenic filters. This function applies
a bank of monogenic filters to an image to obtain the 2D analytic signal
over a number of scales. As in gaborconvolve this can be used as a
pre-processing step for texture analysis, feature detection and
classification, etc.
An explanation of
the implementation of convolution with log-Gabor filters used in the
functions above.
References:
Peter Kovesi,
"Symmetry and Asymmetry From Local Phase". AI'97, Tenth
Australian Joint Conference on Artificial Intelligence. 2 - 4
December 1997. Proceedings - Poster Papers. pp 185-190.
Peter Kovesi,
"Edges Are Not Just Steps". Proceedings of ACCV2002 The
Fifth Asian Conference on Computer Vision, Melbourne Jan
22-25, 2002. pp 822-827.
Non-maxima suppression and hysteresis thresholding
nonmaxsup.m Code for
performing non-maxima suppression for edge images.
nonmaxsuppts.m Code
for performing non-maxima suppression and thresholding of points
generated by a feature/corner detector. It optionally returns
sub-pixel feature locations.
hysthresh.m code for
performing hysteresis thresholding.
smoothorient.m
applies smoothing to an orientation field which can be useful before
applying nonmaximal suppression.
adaptivethresh.m
an implementation of Wellner's adaptive thresholding method.
Edge linking and line segment fitting
image
edges
labeled edges
fitted line segments
edgelink.m edge
linking function that forms lists of connected edge points from a
binary edge image. (Needs findendsjunctions and cleanedgelist below).
drawedgelist.m
plots out a set of edge lists generated by edgelink or lineseg.
edgelist2image.m
transfers edgelist data back into a 2D image array.
lineseg.m forms
straight line segments fitted with a specified tolerance to the lists
of connected edge points.
maxlinedev.m is
also used by lineseg.m to calculate deviations of the edge lists from
the fitted segments.
cleanedgelist.m cleans up a
set of edge lists generated by edgelink or lineseg so that isolated
edges and spurs that are shorter than a minimum length are removed.
step2line.m
Generates a test image where the feature type changes from a step edge
to a line feature from top to bottom, while retaining perfect phase
congruency. This test image indicates the importance of phase
congruency irrespective of the angle at which congruency occurs at
and, up to a point, irrespective of the rate at which the amplitude
spectrum decays with frequency. A gradient based edge detector
produces a double response for all features that have congruence of
phase at angles other than zero (towards the bottom of the test
image). The phase congruency detector marks features with a single
response. The colour coded image was generated by dispfeat.m
Image denoising
noisecomp.m
Code for denoising images. This code differs from standard wavelet
denoising techniques in that it uses non-orthogonal wavelets, and
unlike existing techniques, ensures that phase information is
preserved in the image. Phase information is of crucial importance to
human visual perception. Also, this code does have an
effective way of determining threshold levels automatically.
See the example below, under grey scale transformation and
enhancement, for an example of the use of this function.
shapeletsurf.m
Function reconstructs an estimate of a surface from its surface
normals by correlating the surface normals with that those of a bank
of shapelet basis functions. The correlation results are summed to
produce the reconstruction. The sumation of shapelet basis functions
results in an implicit integration of the surface while enforcing
surface continuity.
Note that the reconstruction is only valid up to a scale factor
(which can be corrected for). However the reconstruction process is
very robust to noise and to missing data values. Reconstructions (up
to positive/negative shape ambiguity) are possible where there is an
ambiguity of pi in tilt values. Low quality reconstructions are also
possible with just slant, or just tilt data alone. However, if you
have full gradient information you are better off with the Frankot
Chellappa algorithm below.
frankotchellappa.m An
implementation of Frankot and Chellappa's algorithm for constructing
an integrable surface from gradient information. If you have full
gradient information in x and y this is probably the best algorithm to
use. It is very simple, very fast and highly robust to noise. If you
have surface normal information in the form of slant and tilt, and you
have an ambiguity of pi in your tilt data, or only have slant, then
try using shapeltsurf.m above.
grad2slanttilt.m
Converts gradient values over a surface to slant and tilt angles.
slanttilt2grad.m
Converts slant and tilt angles over a surface to gradients.
needleplotgrad.m
Generates a needle plot given surface gradients over a surface.
needleplotst.m Generates a
needle plot given slant and tilt values over a surface.
testp.m Generates a
synthetic test surface along with its surface normals for testing
shapeletsurf.
An example of how much 3D shape you can get from very minimal
surface normal information.
Scalogram calculation
scalogram.m
Function to calculate the phase and amplitude scalograms of a 1D
signal. The analysis is done using quadrature pairs of log Gabor
wavelets.
Anisotropic diffusion
anisodiff.m Function
to perform anisotropic diffusion of an image following Perona and
Malik's algorithm. This process smoothes regions while preserving,
and enhancing, the contrast at sharp intensity gradients.
Grey scale transformation and enhancement
extractfields.m
separates fields from a video frame, and optionally interpolates
intermediate lines.
interpfields.m
interpolates lines on a field extracted from a video frame.
greytrans.m allows
you to interactively remap intensity values in a colour or greyscale
image via a mapping function defined by a series of spline points. A
feeble attempt at replicating xv's intensity mapping tool. It
is not as fast but it does operate on floating point images allowing
you to better preserve image fidelity. (Needs remapim.m).
remapim.m is a non-interactive
version of greytrans that allows you to apply an intensity mapping to
a colour or greyscale image using a mapping function determined
experimentally with greytrans. Useful if you want to apply the same
mapping function to a sequence of images.
histtruncate.m
truncates ends of an image histogram. Useful for enhancing images
with outlying values.
Example of using some of
these functions above to enhance a video image.
homomorphic.m
performs homomorphic filtering on an image. One of my favourite image
enhancement techniques. (needs histtruncate.m and normalise.m)
psf.m generates a
variety of point-spread functions. This function can be useful when
manually specifying point-spread functions for Wiener filtering or
with deconvolution functions such as the Richardson-Lucy algorithm
(see the MATLAB image toolbox function deconvlucy.m).
psf2.m is identical
to psf, it just has a different way of specifying the function shape
which may be more convenient for some applications.
imspect.m plots
image amplitude spectrum averaged over all orientations.
freqcomp.m
demonstrates image reconstruction from its Fourier components.
Functions supporting projective geometry
image of beach
rectified beach
homography1d.m
computes the 2x2 1D homography of 3 or more points along a line.
homography2d.m
computes the 3x3 2D homography of 4 or more points in a plane. This
code follows the normalised direct linear transformation algorithm
given by Hartley and Zisserman.
fundmatrix.m
computes the fundamental matrix from 8 or more matching points in a
stereo pair of images using the normalised 8 point algorithm.
affinefundmatrix.m computes the
affine fundamental matrix from 4 or more matching points in a stereo
pair of images.
fundfromcameras.m computes fundamental matrix
given two camera projection matrices.
normalise2dpts.m translates and
normalises a set of 2D homogeneous points so that their centroid is at
the origin and their mean distance from the origin is sqrt(2). This
is used to improve the conditioning of any equations used to solve
homographies, fundamental matrices etc.
hnormalise.m
normalises an array of homogeneous coordinates so that their scale
parameter is 1. Points at infinity are unchanged.
imTrans.m applies a homogeneous
transform to an image.
digiplane.m allows
you to digitise and transform points within a planar region in an
image.
matchbycorrelation.m generates
putative matches between previously detected feature points in two
images by looking for points that are maximally correlated with each
other within windows surrounding each point. Only points that
correlate most strongly with each other in both directions are
returned. This is a simple-minded N2 comparison.
matchbymonogenicphase.m is
similar to matchbycorrelation, but instead matches on oriented phase
values rather than greyscale values. This matcher performs rather
well relative to normalised greyscale correlation. Typically there
are more putative matches found and fewer outliers. There is a
greater computational cost in the pre-filtering stage but potentially
the matching stage is much faster as each pixel is effectively encoded
with only 3 bits. (Though this potential speed is not realized in this
implementation). See testfund
below to see an example of the use of this function.
Inlying matches consistent with fundamental matrix
ransac.m a general purpose
implementation of the RANSAC algorithm. August 2008 This
should be fixed now - sorry for any problems you had
ransacfithomography.m
robustly fits a homography to a set of putatively matched image points.
ransacfitfundmatrix.m robustly
fits a fundamental matrix to a set of putatively matched image points.
This function uses an 8 point fundamental matrix solution.
noiseonf.m generates noise
images with specified amplitude spectra. One can create pleasing
cloud pattern images this way.
cloud9.m creates a movie
sequence of noise images with specified amplitude spectra. Very
relaxing.
derespolar.m Generates
deresolved images in polar coordinates.
polartrans.m Generates a polar
transformation of an image. A linear or logarithmic radius
transformation can be specified.
circsine.m
Generates a test image consisting of a circular sine wave grating.
ASCII Image Generation
matscii.m Function to
generate ASCII images from grey scale images. A bit retro but may have
applications for interesting text messages on your mobile phone!
Homogeneous Transforms
plotframe.m plots a
coordinate frame specified by a homogeneous transform.
normaliseangleaxis.m
normalises angle-axis descriptor so that the angle has a maximum magnitude of pi.
Image Display, Image Writing and Miscellaneous
show.m This function displays
an image, automatically setting the colour map to grey if it is a 2D
image, or leaving it as colour otherwise, and setting the axes to be
'equal'. The image is also displayed as 'TrueSize', that is, pixels
on the screen match pixels in the image. Finally a title
corresponding to the image variable name is added.
showfft.m displays the
amplitude spectrum of an fft.
showlogfft.m displays
the log amplitude spectrum of an fft.
showsurf.m This function wraps up the
commands I usually use to display a surface. The surface is
displayed using SURFL with interpolated shading, in my favourite
colormap of 'copper', with rotate3d on, and axis vis3d set.
imwritesc.m This function
combines image rescaling and writing into the one function. If the
image type is double image values are rescaled to the range
0-1 so that no overflow occurs when writing 8-bit intensity values.
The image format to use is determined by MATLAB from the file ending.
If the image type is of uint8 no rescaling is performed.
matprint.m This function
prints out a matrix using a specified C style format string. Often
you find that MATLAB's default number formats are not what you want.
It is surprising that there is no convenient fine control of output
format. I hope this function helps.
removenan Replaces NaN
values in a matrix with a specified default value. Useful when you
want to prevent NaNs from contaminating and destroying some operation
on an array, for example, an FFT.
fillnan Replaces NaN
values in a matrix with the value in the closest non-Nan pixel.
digipts.m Function to
digitise points in an image. This function uses the cross-hair cursor
provided by GINPUT. I find this is much more useable than the cursor
used by IMPIXEL. In addition each location digitised is marked with a
red '+'.
implace.m Function to place
an image at a specified location within a larger image.
superquad.m generates
parametric surfaces of superquadratics.
supertorus.m generates
parametric surfaces of a supertorus.
You must
listen to The Fundamental
Matrix Song by Daniel Wedge.
August 2008 This
should be fixed now - sorry for any problems you had
