A physical system exposes to us in a real space, while its description often refers to its reciprocal momentum space. A connection between them can be established by exploring patterns of quasiparticles interference (QPI), which is experimentally accessible by Fourier transformation of the scanning tunneling spectroscopy (FT-STS). We here investigate how local and global features of QPI patterns are related to the geometry and topology of electronic structure in the considered physical system. A reduced response function (RRF) approach is developed that can analyze QPI patterns with clear physical pictures. It is justified that the generalized joint density of states, which is the imaginary part of RRF, for studying QPI. Moreover, we reveal that global patterns of QPI may be indicators of topological numbers for gapless systems, and demonstrate that robustness of such indicators against distractive local features of QPI for topological materials with complicated band structures.
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