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2D Polynomial Data Modelling: Version 1.0

This toolbox used discrete orthogonal polynomials to model 2D data, e.g. surfaces and images



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Discrete Orthogonal Toolbox for 2D Data: dop2DBox Version V2.0

July 2013


This toolbox extends the discrete orthogonal toolbox "dopBox" available

to modelling of 2D data sets. Presently the modelling is for datawhich lies on a grid (regular lattice). For example, the tools are particularly well suited for use with images and for regularly scanned surface data.

The toolbox implements a number of 2D algorithms:

The following transformation pair, represent the first Gram and inverse Gram transformations which can deal with images of size > 1000 x 1000 pixels without errors.

dgt2: A 2D Gram polynomial transformation.
idgt2: Inverse 2D Gram polynomial transformation.

dop2DApprox: a 2D Gram polynomial approximation.
dop2DApproxLocal: a local 2D Gram polynomial approximation.

dop2DGradient: A 2D gradient computation with and without spectral regularization.


The toolbox contains four demonstration applications, with corresponding theory:

1) A 2D surface approximation, with the seperation of local surface anomalies from a global surface model.

2) Image illumination correction

3) Regularized and non-regularized gradient computation form surface data.

4) A 2D Gram Transformation and its inverse

The theory behind the surface modelling for real time surface sinpection can be found in the paper:

author = {O'Leary, Paul and Harker, Matthew},
title = {Discrete polynomial moments for real-time geometric surface inspection},
journal = {Journal of Electronic Imaging},
volume = {18},
number = {1},
pages = {013015-013015-13},
year = {2009},
doi = {10.1117/1.2987725},
URL = { +},
eprint = {}

The theory was also extended to circular disks and can be found in:

Author = {Janko, M. and O'Leary, P. and Harker, M.},
Title = {Instrumentation for the 3D Measurement of Circular
Disks and the Quantification of Warpage},
BookTitle = {IEEE International Instrumentation and Measurement Technology Conference},
Address= {Minneapolis, Minnesota, USA },
Publisher = {IEEE},
Pages = {146..150},
Year = {2013} }

This tool requires the dopBox:

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