Figure 3.

Schematic descriptions for the definitions of cavity and cave pocket. (A) A molecular shape X and a spherical probe P. (B) Molecular volume X•P. (C) The space (X•P)^c that a probe P is able to access. The set of probe centers for (X•P)^c is described as (X•P)^c⊝P=X^c⊝P. The shape X^c⊝P is decomposed into connected components. In this case, it is decomposed into two components: an outside component C_out[X^c⊝P] and an inside component I_X(C_k[X^c⊝P]). The frame ∂V[X] is the one-pixel-thick frame of image X. (D) A cavity is defined as I_X(C_k[X^c⊝P])⊕P, which is a dilation of the inside component. (E) The outside component C_out[X^c⊝P] is the set of probe centers where a probe P is able to access from the outside. Its dilation C_out[X^c⊝P]⊕P is the space that a probe P is able to access from the outside. (F) The term (C_out[X^c⊝P]⊕P)^c is the space that a probe P is not able to access from the outside. The cave pocket is defined by the opening of the shape (C_out[X^c⊝P]⊕P)^c∩X^c by the internal probe S. The restriction X^c is added because the inside of X is not the target of the internal probe S.