There are many ways to analyses Hemi-spherical photographs. But the best way is use of associated software with your hemi-view camera. There is free open source software also. These software gives gap size or gap fraction information which can be put in Beer Lambert equation to calculate LAI. hope this will be helpful for you. For further query don't be hesitate.
Gap Light Analyzer GLA: http://www.caryinstitute.org/science-program/our-scientists/dr-charles-d-canham/gap-light-analyzer-gla
There a good review publications, e.g. Jonckheere, I., S. Fleck, K. Nackaerts, B. Muys, P. Coppin, M. Weiss, and F. Baret. 2004. Review of Methods for in situ LAI Determination, Part I: Theories, sensors and hemispherical photography. Agr. For. Meteorol., Vol. 121 (1-2): 19-35. (SCI: 3.668)
the best way to access retrieval of leaf aera index through hemispherical is to real Li-Cor LAI-2000 introduction or TRAC introduction, which both are relatively mature method to calculate LAI.
or , you can find some papers as following,
Hemispherical photography simulations with an architectural modelto assess retrieval of leaf area index