ARPGE was developed in 2006 in order to reconstruct the prior parent grains from Electron Back-Scatter Diffraction (EBSD) maps acquired on fully transformed materials [1,2]. At that time, parent reconstruction from EBSD was already possible, but only for bcc-hcp transformation in titanium or zirconium alloys  and was not effective for fcc-bcc transformation in martensitic or bainitic steels.
ARPGE is based on a rigorous crystallographic analysis the orientational variants and their specific misorientations (operators). The variants are defined by the cosets on the subgroup of symmetries that are common to the parent and daughter crystals, and the operators are the double-cosets. Their number is given by Lagrange and Burnside formula, respectively. The algebraic structure formed by the variants and operators is a groupoid . A computer program called GenOVa was written to calculate the elements of the groupoid for any structural transformation; it just needs the information of point groups of the parent and daughter phases and the orientation relationship . The theoretical groupoid composition table generated by GenOVa is the fundamental element that is used to treat the experimental EBSD maps and reconstruct the parent grains.
ARPGE can reconstruct the austenitic grains in martensitic and bainitic steels [1,2], the parent beta grains in titanium and zirconium alloys , the parent cubic grains in monoclinic zirconia  etc. ARPGE also offers the possibility to plot maps of orientation relationship (and not only orientations) in martensitic steels . It also helps the user to quantify variants selection in steels by coloring the variant groups (close-packed plane crystallographic packets, close-packed direction packets, Bain packets, plate groups). ARPGE also treats the case of multiple twinning in fcc materials in order to quantify the effect of thermomechanical treatments on the twin fractions (grain boundary engineering) .
ARPGE is fully automatic, fast and easy to use, but it also suffers some limitations. Highly deformed materials are difficult to reconstruct; the parent texture and grain sizes are well rendered but the exact parent boundaries are badly defined and are sensitive to the reconstruction parameters. Examples will be shown on ausformed steels. Some twins in prior austenite can be missed, but using appropriate orientation relation helps to reduce the problem. An independent evaluation of ARPGE on low carbon steels can be found in ref. . Since 2006, other computer programs devoted to parent reconstruction have been developed by laboratories and industries all over the word, each with their specificities and efficiencies; among them one can cite those developed by Miyamoto et al. , Germain et al. , Abassi et al. , Bernier et al. .
 C. Cayron, B. Artaud, L. Briottet, Reconstruction of parent grains from EBSD data, Mater. Charact 57 (2006) 386-401.
 C. Cayron, ARPGE : a computer program to automatically reconstruct the parent grains from electron backscatter diffraction data, J. Appl. Cryst. 40 (2007) 1183-1188.
 N. Gey, M. Humbert, Specific analysis of EBSD data to study the texture inheritance due to the bcc-hcp phase transformation, J. Mater. Sci. 38 (2003) 1289-1294.
 C. Cayron, Groupoid of orientational variants, Acta Cryst. A62 (2006) 21-40.
 C. Cayron, GenOVa : a computer program to generate orientational variants, J. Appl. Cryst. 40 (2007) 1179-1182.
 C. Cayron, T. Douillard, A. Sibil, G. Fantozzi, Reconstruction of the cubic and tetragonal grains from electron backscatter diffraction maps of monoclinic zirconia, J. Am. Ceram. Soc. 93 (2010) 2541-2544.
 C. Cayron, EBSD imaging of orientation relationships and variants groupings in different martensitic alloys and Widmanstätten iron meteorites, Mater. Charact. 94 (2014) 93-110.
 C. Cayron, Quantification of multiple twinning in face centred cubic materials, Acta Mater. 59 (2011) 252-262.
 S. Weyand, D. Britz, D. Rupp, F. Mücklich, Investigation of austenite evolution in low-steel by combining thermos-mechanical simulation and EBSD data, Mater. Perf. Charact. 4 (2015) 322-340.
 G. Miyamoto, N. Iwata, N. Takayama, T. Furuhara, Mapping the parent austenite orientation reconstructed from the orientation of martensite by EBSD and its application to ausformed martensite. Acta Mater. 58 (2010) 6393–403.
 L. Germain, N. Gey, R. Mercier, P. Blaineau , M. Humbert, An advanced approach to reconstructing parent orientation maps in the case of approximate orientation relations: application to steels. Acta Mater. 60 (2012) 4551–62.
 M. Abbasi, T.W. Nelso, C.D. Sorensen, L. Wei, An approach to prior austenite reconstruction, Mater. Charact. 66 (2012) 1-8.
 N. Bernier, L. Bracke, L. Malet, S. Godet, An alternative to the crystallographic reconstruction of austenite in steels, Mater. Charact. 89 (2014) 23–32