1. A method for data deduplication of an initial snapshot of a data set in a storage system by a processor, comprising: building an intra-snapshot similarity index, inclusive only of representations of the data inside the initial snapshot; using the intra-snapshot similarity index for deduplication of the initial snapshot in a chain of a plurality of snapshots by first using only the representations of the data within the intra-snapshot similarity index of the initial snapshot to perform the deduplication of the initial snapshot prior to using a global similarity index to perform the deduplication; wherein the global similarity index is used to perform the deduplication of the initial snapshot subsequent to using the intra-snapshot similarity index when a deduplication threshold is not met using the intra-snapshot similarity index; and merging the intra-snapshot similarity index with the global similarity index by performing each of: structurally merging the intra-snapshot index into the global similarity index, bulk inserting entries of the intra-snapshot index into the global similarity index when unable to structurally merge the intra-snapshot index into the global similarity index, and performing the merging of the intra-snapshot index with the global similarity index when deduplication processing of the initial snapshot is complete.