Fig 1.
Overview of the proposed FlexClustS and FlexClustB algorithms.
Table 1.
Calibration results of simulated data sets using MixSim.
Table 2.
Average performance measures of the 3 simulated data sets.
Fig 2.
True parameter of means and covariances (‘x’ and red line) compared to the FlexClustS model (‘+’ and black line).
Comparison after processing: a) 1 sample, b) 3 samples, and c) whole data set, in one of the experiments of FlexClustS [500]. (Note: ‘x’ and ‘+’ represent means, and covariances are visualized by 90% normal tolerance ellipsoids).
Fig 3.
True clusters structure (scatterplot of 10% of the total data points), and the examples of cluster structure obtained by three algorithms.
(a) FlexClustS–identify the correct 7 clusters, (b) Strategy III—miss out cluster 6 but identify superfluous clusters, (c) sufficient EM—miss out cluster 6 but identify superfluous clusters at cluster 1 and 2.
Fig 4.
Comparison of computation time of the four algorithms for the simulated data.
Computation Time in the stages of: (a) scaled down data clustering, (b) extend to all data clustering. (See Table 1 for the values of n and np).
Fig 5.
Accumulated stage by stage computational time of FlexClustS, Strategy III, FlexClustB and sufficient EM.
(a) Simulated data set 1, (b) Simulated data set 2, (c) Simulated data set 3. (Note: FlexClustS and FlexClustB consists of 3 stages: (1) scan through and selection, (2) multiple samples clustering, (3) measure similarity and perform domain adaptation to classify all the descriptors. Strategy III consists of 2 stages: (1) one sample clustering, (2) EM to whole data set. Sufficient EM consists of 2 stages: (1) cluster whole data set by k-means, (2) EM to sufficient statistics obtained from stage (1)).
Fig 6.
Structural similarity indices (SSI) of images being processed from 10%N to 100%N using FlexClustS.
Table 3.
Structural similarity indices (SSI) for images processed through sampling.
Fig 7.
Comparison of St Paulia image.
(a) Ground true (SSI = 1). Example of images obtained by: (b) FlexClustS [n = 1%N] (SSI = 0.7408), (c) FlexClustS [n = 2%N] (SSI = 0.7697), (d) Strategy III [n = 1%N] (SSI = 0.6970), (e) Strategy III [n = 2%N] (SSI = 0.7086).
Fig 8.
Close-up performance comparison of St Paulia image.
(a) ground truth (SSI = 1), (b) FlexClustS [n = 1%N] (SSI = 0.7408), (c) FlexClustS [n = 2%N] (SSI = 0.7697), (d) Strategy III [n = 1%N] (SSI = 0.6970), and (e) Strategy III [n = 2%N] (SSI = 0.7086).
Fig 9.
(a) Ground true (SSI = 1). Example of images obtained by: (b) FlexClustS [n = 1%N] (SSI = 0.2413), (c) FlexClustS [n = 2%N] (SSI = 0.2524), (d) Strategy III [n = 1%N] (SSI = 0.2351), and (e) Strategy III [n = 2%N] (SSI = 0.2388).
Fig 10.
Close-up performance comparison of cytology image.
(a) Ground truth (SSI = 1), (b) FlexClustS [n = 1%N] (SSI = 0.2413), (c) FlexClustS [n = 2%N] (SSI = 0.2524), (d) Strategy III [n = 1%N] (SSI = 0.2351), and (e) Strategy III [n = 2%N] (SSI = 0.2388).
Fig 11.
(a) Ground true (SSI = 1). Example of images obtained by: (b) FlexClustS [n = 0.5%N] (SSI = 0.6145), (c) FlexClustS [n = 1%N] (SSI = 0.6429), (d) Strategy III [n = 0.5%N] (SSI = 0.6708), and (e) Strategy III [n = 1%N] (SSI = 0.6633).
Fig 12.
(a) Ground true on (SSI = 1). Example of images obtained by: (b) FlexClustS [n = 0.5%N] (SSI = 0.6859), (c) FlexClustS [n = 1%N] (SSI = 0.6923), (d) Strategy III [n = 0.5%N] (SSI = 0.6739), and (e) Strategy III [n = 1%N] (SSI = 0.6702).
Fig 13.
Close-up performance comparison of sailboat image.
(a) Ground truth (SSI = 1), (b) FlexClustS [n = 0.5%N] (SSI = 0.6859), (c) FlexClustS [n = 1%N] (SSI = 0.6923), (d) Strategy III [n = 0.5%N] (0.6739), and (e) Strategy III [n = 1%N] (SSI = 0.6702).
Fig 14.
Comparison of San Diego image.
(a) Ground true on (SSI = 1). Example of images obtained by: (b) FlexClustS [n = 0.5%N] (SSI = 0.6957), (c) FlexClustS [n = 1%N] (SSI = 0.7012), (d) Strategy III [n = 0.5%N] (SSI = 0.7179), and (e) Strategy III [n = 1%N] (SSI = 0.7240).
Table 4.
Structural similarity indices (SSI) for images processed by dividing image into blocks.
Fig 15.
Comparison of St Paulia image.
(a) Ground true (SSI = 1). Example of images obtained by FlexClustB on image division into: (b) 8x2 blocks (SSI = 0.8318), and (c) 16x2 blocks (SSI = 0.8047). Example of images obtained by sufficient EM on image division into: (d) 8x2 blocks, 60 sets of sufficient statistics per block (SSI = 0.6315), and (e) 16x2 blocks, 10 sets of sufficient statistics per block (SSI = 0.7236).
Fig 16.
(a) Ground true (SSI = 1). Example of images obtained by FlexClustB on image division into: (b) 5x4 blocks (SSI = 0.3169), and (c) 10x8 blocks (SSI = 0.3141). Example of images obtained by sufficient EM on image division into: (d) 5x4 blocks, 60 sets of sufficient statistics per block (SSI = 0.2111), and (e) 10x8 blocks, 5 sets of sufficient statistics per block (SSI = 0.1591).
Fig 17.
(a) Ground true (SSI = 1). Example of images obtained by FlexClustB on image division into: (b) 8x8 blocks (SSI = 0.8332), and (c) 16x16 blocks (SSI = 0.8293). Example of images obtained by sufficient EM on image division into: (d) 8x8 blocks, 65 sets of sufficient statistics per block (SSI = 0.6786), and (e) 16x16 blocks, 10 sets of sufficient statistics per block (SSI = 0.6726).
Fig 18.
(a) Ground true on (SSI = 1). Example of images obtained by FlexClustB on image division into: (b) 8x8 blocks (SSI = 0.8687), and (c) 16x16 blocks (SSI = 0.8826). Example of images obtained by sufficient EM on image division into: (d) 8x8 blocks, 65sets of sufficient statistics per block (SSI = 0.7115), and (e) 16x16 blocks, 3 sets of sufficient statistics per block (SSI = 0.5506).
Fig 19.
Close-up performance comparison of sailboat image.
(a) Ground truth (SSI = 1), (b) FlexClulstB, 8x8 blocks (SSI = 0.8687), (c) FlexClust, 16x16 blocks (SSI = 0.8862), (d) sufficient EM, 8x8 blocks (SSI = 0.7115), and (e) sufficient EM, 16x16 blocks (SSI = 0.5506).
Fig 20.
Comparison of San Diego image.
(a) Ground true on (SSI = 1). Example of images obtained by FlexClustB on image division into: (b) 8x8 blocks (SSI = 0.8423), and (c) 16x16 blocks (SSI = 0.7816). Example of images obtained by sufficient EM on image division into: (d) 8x8 blocks, 65 sets of sufficient statistics per block (SSI = 0.7435), and (e) 16x16 blocks, 10 sets of sufficient statistics per block (SSI = 0.6297).
Table 5.
Average number of clusters obtained for the 5 images.
Table 6.
Mean time (in secs) for image processing by sampling using FlexclustS and Stratgy III.
Table 7.
Mean time (in secs) for image processing by block using FlexclustB and sufficient EM.
Fig 21.
Comparison of structural similarity index (SSI) and computational time.
(a) FlexClustS (based on 10%N) and Strategy III, (b) FlexClustB and sufficient EM.