Fig. 1. Computation of index function

Fig. 2. Weight computation of feature points

Fig. 3. Homomorphic shrinkage algorithm. (a) Before simplification; (b) after simplification

Fig. 4. Schematic of retention index

Fig. 5. Flow chart of the proposed algorithm

Fig. 6. Raw data. (a) kerolamp model; (b) helix model

Fig. 7. Delaunay triangulation construction. (a) kerolamp model; (b) helix model

Fig. 8. Piecewise linear falling Morse complex extracted by the proposed algorithm. (a) kerolamp model; (b) helix model

Fig. 9. Piecewise linear falling Morse complex extracted by the method in Ref.[24]. (a) kerolamp model; (b) helix model

Fig. 10. Feature extraction results for kerolamp model in different thresholds. (a) λ=0.8,X_T =0.23; (b) λ=0.8,X_T =0.3; (c) λ=0.8,X_T =0.32

Fig. 11. Feature extraction results for helix model in different thresholds. (a) λ=0.7,X_T=0.15; (b) λ=0.7,X_T=0.2; (c) λ=0.7,X_T=0.22

Fig. 12. Feature extraction results for model 1 in different noise levels. (a) 0 dB; (b) 10 dB; (c) 20 dB; (d) 50 dB