MATLAB and Octave Functions
for Computer Vision and Image Processing

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!

Please report any bugs and/or suggest enhancements to

Cheers,
Peter Kovesi

Note that I develop my code under Mac OS X.

• How to cite this site
• MIT License
• Notes on using Octave - almost all of these functions run under Octave. With the release of Octave 3 you have a very viable alternative to MATLAB.

Legend for MATLAB/Octave compatibility

• Runs under MATLAB and Octave.
• Only runs under MATLAB.
• Not tested under Octave (yet).

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Feature detection via Phase Congruency

Phase congruency is an illumination and contrast invariant measure of feature significance. Unlike gradient based feature detectors, which can only detect step features, phase congruency correctly detects features at all kind of phase angle, and not just step features having a phase angle of 0 or 180 degrees.

• phasecongmono.m This function computes phase congruency via monogenic filters. It has excellent speed and much reduced memory requirements compared to the other phase congruency functions below. However you may prefer the output from phasecong3's oriented filters.
• phasecong3.m This function supersedes phasecong2.m and phasecong.m being faster and requiring less memory.
  • Deprecated: phasecong.m Original code for calculating phase congruency in an image. This function also returns a feature type image. Note this function is superseded by phasecong2.m and phasecong3.m and is only here for reference.
  • Deprecated: phasecong2.m Phase congruency code that combines edge and corner detection, and provides better localization. Note this function is superseded by phasecong3.m and phasecongmono.m and is only here for reference.

• 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!). (Updated May 2009)
• phasesymmono.m This function computes phase symmetry via monogenic filters. Has excellent speed and much reduced memory requirements compared to phasesym.m However you may prefer the output from phasesym's oriented filters.
• 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 bank used 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, "Image Features From Phase Congruency". Videre: A Journal of Computer Vision Research. MIT Press. Volume 1, Number 3, Summer 1999.
• 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.
• Peter Kovesi, "Phase Congruency Detects Corners and Edges". The Australian Pattern Recognition Society Conference: DICTA 2003. December 2003. Sydney. pp 309-318.

Spatial feature detection

• canny.m Canny edge detector incorporating modifications suggested by Fleck.
• harris.m Harris corner detector.
• fastradial.m An implementation of Loy and Zelinski's fast radial feature detector.

Reference:

• Scanned images of my photocopy of Harris and Stephens' paper 'A Combined Corner and Edge Detector'.

Integral Images

• integralimage.m computes integral image of an image.
• integralfilter.m performs filtering using an integral image.
• intfilttranspose.m transposes an integral image filter specification.
• integaverage.m performs averaging filtering using an integral image. Computation cost is independent of averaging filter size.
• integgausfilt.m This function approximates Gaussian filtering by repeatedly applying integaverag.m . This allows smoothing at a very low computational cost that is independent of the Gaussian size.
• solveinteg.m This function is used by integgausfilt.m to solve for the multiple averaging filter widths needed to approximate a Gaussian of desired standard deviation.

Reference:

• Draft note describing high speed approximate Gaussian filtering via integral images.

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.
• findendsjunctions.m finds line junctions and endings in a line/edge image.
• 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.
• Example of using these functions above.

Test grating for edge detection

Test image

Canny edge image

Phase congruency

Colour coded for feature type

• 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.

Reference:

• Peter Kovesi, "Phase Preserving Denoising of Images". The Australian Pattern Recognition Society Conference: DICTA'99. December 1999. Perth WA. pp 212-217.

Surface normals to Surfaces

Surface Normals

Surface Reconstruction

• 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.

Reference:

• Peter Kovesi, "Shapelets Correlated with Surface Normals Produce Surfaces". 10th IEEE International Conference on Computer Vision. Beijing. pp 994-1001. 2005
• PowerPoint Slides
• 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.
• normalise.m rescales image values to 0-1.
• adjcontrast.m adjusts image contrast using sigmoid function.
• adjgamma.m adjusts image gamma.
• 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. However you should note that many surveillance systems are close to being legally blind.
• See Video Surveillance: Legally Blind? DICTA 2009 Melbourne.

Frequency domain transformations

• lowpassfilter.m constructs low-pass Butterworth filter.
• highpassfilter.m constructs high-pass Butterworth filter.
• highboostfilter.m constructs high-boost Butterworth filter.
• bandpassfilter.m constructs band-pass Butterworth filter.
• 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.
• equalAngleConstraint.m Affine transform constraints given two equal angles.
• knownAngleConstraint.m Affine transform constraints given a known angle.
• lengthRatioConstraint Affine transform constraints given a length ratio.
• circleintersect.m Finds intersection of two circles. Use this function to solve for affine transformation constraints.
• circle.m Draws a circle.
• hcross.m Homogeneous cross product, result normalised to s = 1.
• hline.m Plot 2D lines defined in homogeneous coordinates.
• homoTrans 2D homogeneous transformation of points/lines.
• plotPoint.m Plots point with specified mark and optional text label.

• If you are using these functions above you should look at Andrew Zisserman's MATLAB Functions for Multiple View Geometry
  Also, you must listen to The Fundamental Matrix Song by Daniel Wedge.

Matching

• 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.

Model fitting and Robust estimation

Putative matches obtained by matchbycorrelation.m

Inlying matches consistent with fundamental matrix

• ransac.m a general purpose implementation of the RANSAC algorithm.
• 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.
• ransacfitfundmatrix7.m robustly fits a fundamental matrix to a set of putatively matched image points. This function requires Andrew Zisserman's 7 point fundamental matrix code available from: MATLAB Functions for Multiple View Geometry
• ransacfitaffinefund.m robustly fits an affine fundamental matrix to a set of putatively matched image points.
• ransacfitplane.m robustly fits a plane to 3D data points.
• ransacfitline.m robustly fits a line to 3D data points.
• iscolinear.m tests if 3 points are colinear, used by ransacfitplane and ransacfithomography.
• fitline.m least squares fit of a line to 2D data points.
• fitline3d.m least squares fit of a line to 3D data points. Contributed by Felix Duvallet.
• fitplane.m least squares fit of a plane to 3D data points.
• testfitplane example of using ransacfitplane.m
• testfitline example of using ransacfitline.m
• testfund example of using ransacfitfundmatrix.m
• testhomog example of using ransacfithoography.m
• randomsample a basic replacement for randsample to be used with ransac.m should you not have the statistics toolbox, or are using Octave.
• Example of using these functions above to find the fundamental matrix.

Fingerprint enhancement

• ridgesegment.m identifies ridge-like regions of a fingerprint image. It also normalises the intensity values of the image.
• ridgeorient.m estimates the local orientation of ridges in a fingerprint.
• plotridgeorient.m plots ridge orientations calculated by ridgeorient.
• ridgefreq.m estimates the local ridge frequency across a fingerprint image.
• freqest.m estimates the ridge frequency within a small block of an image. This is used by ridgefreq.
• ridgefilter.m enhances a fingerprint image using oriented filters.
• Example of using these functions above.

Interesting images

• 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.
• trans.m homogeneous tranlation matrix.
• rotx.m homogeneous matrix for rotation about x-axis.
• roty.m homogeneous matrix for rotation about y-axis.
• rotz.m homogeneous matrix for rotation about z-axis.
• homotrans.m homogeneous transformation of points/lines
• invht.m optimized inverse of homogeneous transformation matrix
• inveuler.m solves for euler angles given a homogeneous transform.
• invrpy.m solves for roll, pitch, yaw angles given a homogeneous transform.
• dhtrans.m calculates the 4x4 homogeneous Denavit Hartenberg matrix given link parameters of joint angle, length, joint offset, and twist.

Quaternions

• newquaternion.m construct quaternion from specified angle and axis.
• matrix2quaternion.m converts 4x4 homogeneous rotation matrix to quaternion
• quaternion2matrix.m converts quaternion to a 4x4 homogeneous transformation matrix.
• quaternionrotate.m uses quaternion to rotate vectors.
• quaternionproduct.m computes quaternion product.
• quaternionconjugate.m computes quaternion conjugate.
• vector2quaternion.m embeds a 3-vector in a quaternion.

Angle-Axis Descriptors

• newangleaxis.m constructs angle-axis descriptor from specified angle and axis.
• matrix2angleaxis.m converts homogeneous rotation matrix to angle-axis description
• angleaxis2matrix.m converts angle-axis descriptor to 4x4 homogeneous transformation matrix.
• angleaxisrotate.m uses angle axis descriptor to rotate vectors
• 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.
• cubicroots.m computes the real roots of a cubic.
• rgb2lab.m RGB to L*a*b* colour conversion.