IEEE Signal Processing - July 2018 - 40

Table 3. The average F1 score using the CDnet data set for the comparison of provable, heuristics, and heuristics with specific constraints methods for
background subtraction. Time is shown for a video having 320 × 240 resolution of 8, 000 frames. The best and second-best performing methods are
shown in red and blue, respectively.
Provable Methods

Baseline

DB

Camera Jitter

Shadow

Thermal

IOM

Average

Time (s/frame)

PCP (batch); Figure 5(c); [4], [5]

0.75

0.69

0.62

0.73

0.65

0.48

0.65

4.19

AltProj (batch); [8]

0.78

0.71

0.60

0.76

0.69

0.58

0.68

2.38

NO-RMC (batch); Figure 5(o); [17]

0.71

0.64

0.64

0.66

0.71

0.50

0.64

2.85

RPCA-GD (batch); Figure 5(f); [10]

0.74

0.62

0.68

0.75

0.66

0.49

0.65

2.46

Simple-ReProCS (online); [9], [29]

0.77

0.77

0.69

0.71

0.74

0.70

0.73

0.74

Mod-PCP (online); [30]

0.75

0.64

0.70

0.65

0.69

0.70

0.68

0.44

Heuristics Methods

Baseline

DB

Camera Jitter

Shadow

Thermal

IOM

Average

Time

GRASTA (online); Figure 5(k); [50]

0.66

0.35

0.43

0.52

0.42

0.35

0.45

1.16

3TD (batch); Figure 5(g); [62]

0.88

0.75

0.72

0.68

0.78

0.55

0.72

2.17

2PRPCA (batch); Figure 5(u); [63]

0.92

0.79

0.81

0.80

0.76

0.65

0.78

1.63

GoDec (batch); Figure 5(d); [37]

0.77

0.58

0.48

0.51

0.62

0.38

0.55

1.56

OR-PCA (online); [47]

0.62

0.45

0.36

0.52

0.66

0.59

0.53

0.17

pROST (online); Figure 5(h); [51]

0.79

0.59

0.79

0.70

0.58

0.48

0.65

2.03

Probabilistic robust matrix factorization; Figure
5(e); [64]

0.92

0.77

0.85

0.88

0.83

0.48

0.78

2.40

Heuristics Methods with Specific Constraints

Baseline

DB

Camera Jitter

Shadow

Thermal

IOM

Average

Time

modified-ReProCS (online); Figure 5(l); [12]

0.80

0.76

0.72

0.75

0.77

0.69

0.74

0.61

incPCP (online); Figure 5(i); [52]

0.81

0.71

0.78

0.74

0.70

0.75

0.74

0.41

OR-PCA-illum (online); Figure 5(t); [74]

0.86

0.75

0.70

0.74

0.76

0.56

0.72

0.22

MSCL (batch); Figure 5(x); [65]

0.87

0.85

0.83

0.82

0.82

0.80

0.83

1.68

DECOLOR (batch); Figure 5(v); [66]

0.92

0.70

0.68

0.83

0.70

0.59

0.73

1.88

LSD (batch); Figure 5(p); [67]

0.92

0.71

0.78

0.81

0.75

0.67

0.77

1.43

TVRPCA (batch); Figure 5(m); [68]

0.84

0.55

0.63

0.71

0.69

0.57

0.66

1.48

SRPCA (batch); Figure 5(n); [69]

0.82

0.84

0.78

0.77

0.79

0.80

0.80

0.59

RMAMR (batch); Figure 5(j); [70]

0.89

0.82

0.75

0.73

0.75

0.66

0.76

1.32

GFL (batch); Figure 5(w); [71]

0.83

0.74

0.78

0.82

0.76

0.59

0.75

2.40

GOSUS (online); Figure 5(q); [53]

0.90

0.79

0.82

0.84

0.80

0.74

0.81

0.89

COROLA (online); Figure 5(s); [72]

0.85

0.86

0.82

0.78

0.80

0.71

0.80

0.39

OMoG+TV (online); Figure 5(r); [73]

0.85

0.76

0.78

0.68

0.70

0.71

0.74

0.19

Non-RPCA Methods

Baseline

DB

Camera Jitter

Shadow

Thermal

IOM

Average

Time

PAWCS; [75]

0.88

0.85

0.78

0.86

0.80

0.74

0.81

2.82

SuBSENSE; [76]

0.91

0.78

0.78

0.88

0.78

0.63

0.79

1.89

LOBSTER; [77]

0.87

0.74

0.80

0.72

0.79

0.72

0.75

3.7

ones get classified as small noise w t . Moreover, as we explain
later (see Remark 3.5), the requirement can be relaxed further.
The looser requirement on outlier fractions per row means
that ReProCS can tolerate slow moving or occasionally static
objects better than other approaches (does not confuse these
for the background).
Another approach that can solve RST is modified-PCP
[30]. This was designed as a solution to the problem of
RPCA with partial subspace knowledge [30]. It solves RST
40

by using the previous subspace estimate as the "partial subspace knowledge."

Dynamic versus static robust principal component analysis
While RST or dynamic RPCA is a different problem than static
RPCA (it assumes a time-varying subspace and slow subspace
change), from the point of view of applications, especially
those for which a natural time sequence exists, e.g., video analytics for videos from static camera(s) or dynamic MRI-based

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