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In CAN_EYE, the clumping index is computed using the Lang and Yueqin (1986) logarithm gap fraction averaging method. The principle is based on the assumption that vegetation elements are locally assumed randomly distributed. Each zenithal ring is divided into groups (called cells) of individual pixels. The size of the individual cells must be chosen by making a  compromise between two criterions:

• it should be large enough so that the statistics of the gap fraction are meaningful
• it should be small enough so that the assumption of randomness of leaf distribution within the cell is valid.

For each cell, CAN-EYE computes the gap fraction P_o as well as its logarithm. If there is no gap in the cell (only vegetation), the cell gap fraction P_oCELL is assumed to be equal to a P_oSAT value derived from the classical Poisson law, using a prescribed PAI_SAT value. P_oCELL as well as ln(P_oCELL) are then weighted averaged over the azimuth and over the images for each zenithal ring. The weights take into account the masked areas (the more masked pixels, the lower weight). The ratio of these two averaged quantities provides the clumping parameter CF for each zenithal ring:

CF=av. mean(log(Po_CELL)) / log(av.mean(Po_CELL))

Reference

Lang, A.R.G. (1986). Leaf area and average leaf angle from direct transmission of sunlight. Aust. J. Bot., 34, 349-355Lang, A.R. (1991). Application of some of Cauchy's theorems to estimation of surface areas of leaves, needles, and branches of plants, and light transmittance. Agric. For. Meteorol., 55, 191-212
Lang, A.R.G., & McMurtrie, R.E. (1992). Total leaf areas of single trees of Eucalyptus grandis estimated from transmittances of the sun's beam. Agric. For. Meteorol., 58, 79-92