We provide an ejjicient algorithm for the rooted binary tree isomorphism problem under the operation of graph minors (restricted version). This arwes as a result of corresponding lung volumes during different phases of breathing and in comparing normal and diseased lungs. Given two rooted binary trees T1 = (Vl, El, WI ) and T2 = (V., E2, W2 ) (W’I, W2 correspond to 3’D coordinates WI, W2 : V– > R3) as inputs, we want to obtain a oneto-one matching function f of nodes in T1 to T2 such that the edges emanating from V1 in TI map to edgedisjoint paths emanating from f(vl ) in T2. In addition to this topology match, WI and W2 are used to closely match the geometric properties of these trees i.e. the Euclidean proximity of mapped nodes, similar values m edge lengths and angles between adjacent edges. In general, nodes in Tz can be viewed as a non-uniform displacement (spheres of varying radii) of nodes in T1. If we consider only the topology match of TI and Tz (i, e. mapping edges of TI to edge-disjoint paths in T2 without considering WI and W2), we provide a O(IV1 I * IV2 I) dynamzc programming solution to the existence of function f. This is equivalent to checking if TI and T2 are isomorphic under graph minors. Since there could exist exponential number of distinct trees of T2 that can be reduced to TI under graph minors, we reduce this search space by incorporating the geometric constraints into our matching algorithm. T1 and T2 are computed by a twopass central axis algorithm on lung volumes.