Decision tree (DT) induction has been widely used in different pattern classification. However, most traditional DTs have the disadvantage that they consider only non-spatial attributes (ie, spectral information) as a result of classifying pixels, which can result in objects being misclassified. Therefore, some researchers have proposed a co-location decision tree (Cl-DT) method, which combines co-location and decision tree to solve the above the above-mentioned traditional decision tree problems. Cl-DT overcomes the shortcomings of the existing DT algorithms, which create a node for each value of a given attribute, which has a higher accuracy than the existing decision tree approach. However, for non-linearly distributed data instances, the euclidean distance between instances does not reflect the true positional relationship between them. In order to overcome these shortcomings, this paper proposes an isometric mapping method based on Cl-DT (called, (Isomap-based Cl-DT), which is a method that combines heterogeneous and Cl-DT together. Because isometric mapping methods use geodetic distances instead of Euclidean distances between non-linearly distributed instances, the true distance between instances can be reflected. The experimental results and several comparative analyzes show that: (1) The extraction method of exposed carbonate rocks is of high accuracy. (2) The proposed method has many advantages, because the total number of nodes, the number of leaf nodes and the number of nodes are greatly reduced compared to Cl-DT. Therefore, the Isomap -based Cl-DT algorithm can construct a more accurate and faster decision tree.