BUUHWE_2D.plot: Graphical representation of the 2D-BUUHWE (or SHAH) of an...
In Bagidis: BAses GIving DIStances

Description Usage Arguments Details Value Note Author(s) References See Also Examples

View source: R/BUUHWT_2D_Graph_v2.r

Graphical representation of the 2D-BUUHWE or SHAH transform of an image. The representation of the process is either through the evolving network representation or through the successively built basis matrices of the Unbalanced Haar wavelet basis associated to the transform.

BUUHWE_2D.plot(out.BUUHWE_2D, Evol = TRUE)
SHAH.plot(out.BUUHWE_2D, Evol = TRUE)
BUUHWE_2D_Stepwise(Data,Plot)
SHAH_Stepwise(Data,Plot)

`out.BUUHWE_2D`	the result of `BUUHWE_2D` or `SHAH` applied to an image.
`Evol`	Logical. Should the evolution of the complete network be represented? Default is TRUE and is more informative but applies only for images of reasonable size (otherwise graphics are not readable). if FALSE, only segments linking the input and output nodes at each step are represented and superimposed.
`Data`	a matrix encoding an image
`Plot`	Logical. Should all the basis matrices be represented? Default is TRUE. Otherwise not representation is provided, but the matrices are returned by the function so that they can be represented separetely.

See BAGIDIS-package for an overview about the BAGIDIS methodology and References for details, in particular Timmermans (2012), Chapter 4, and Timmermans and Fryzlewicz (2012).

BUUHWT_2D_Stepwise or SHAH_Stepwise returns a list with

`basis`	An array of the basis matrices of the 2D-BUUHWT (SHAH)
`details`	the detail coefficients for ranks NM-1 to 1 (with N*M the dimension of the image) (i.e. in their ordre of construction)
`d0`	the detail coefficients for ranks 0
`im`	the initial image
`labels.hist`	the evolution of the labels associated to the pixels

The function are mainly used for their side-effect Plot=TRUE. Functions BUUHWE_2D.plot or SHAH.plot are only used for their side-effect.

The equivalent function for curves is semimetric.BAGIDIS.

Catherine Timmermans, Institute of Statistics, Biostatistics and Actuarial Sciences, UCLouvain, Belgium.

Contact: catherine.timmermans@uclouvain.be

The main references are

Timmermans C., 2012, Bases Giving Distances. A new paradigm for investigating functional data with applications for spectroscopy. PhD thesis, Universite catholique de Louvain. http://hdl.handle.net/2078.1/112451
Timmermans C. and von Sachs R., 2015, A novel semi-distance for investigating dissimilarities of curves with sharp local patterns, Journal of Statistical Planning and Inference, 160, 35-50. http://hdl.handle.net/2078.1/154928
Fryzlewicz P. and Timmermans C., 2015, SHAH: Shape Adaptive Haar wavelets for image processing. Journal of Computational and Graphical Statistics. (accepted - published online 27 May 2015) http://stats.lse.ac.uk/fryzlewicz/shah/shah.pdf
Timmermans C., Delsol L. and von Sachs R., 2013, Using BAGIDIS in nonparametric functional data analysis: predicting from curves with sharp local features, Journal of Multivariate Analysis, 115, p. 421-444. http://hdl.handle.net/2078.1/118369

Other references include

Girardi M. and Sweldens W., 1997, A new class of unbalanced Haar wavelets that form an unconditional basis for Lp on general measure spaces, J. Fourier Anal. Appl. 3, 457-474
Fryzlewicz P., 2007, Unbalanced Haar Technique for Non Parametric Function Estimation, Journal of the American Statistical Association, 102, 1318-1327.
Timmermans C., von Sachs, R. , 2010, BAGIDIS, a new method for statistical analysis of differences between curves with sharp patterns (ISBA Discussion Paper 2010/30). Url : http://hdl.handle.net/2078.1/91090
Timmermans, C. , Fryzlewicz, P., 2012, SHAH: Shape-Adaptive Haar Wavelet Transform For Images With Application To Classification (ISBA Discussion Paper 2012/15). Url: http://hdl.handle.net/2078.1/110529

BUUHWE_2D, SHAH, semimetric.BAGIDIS.

im = rbind(c(1,2,3), c(5,3,2), c(1,1,2))
im2 = rbind(c(1,1,5), c(5,5,2), c(1,0,0))

SHAH(im)
SHAH_Stepwise(im)

SHAH.plot(SHAH(im))

SHAH.plot(SHAH(im),Evol=FALSE)

SHAH_Stepwise(im)$details
Signature_2D(SHAH(im))