<H1>8. Results</H1>
        In this section, we report the results of simulation parameters obtained using our technique applied to four fabrics: linen, fleece, satin and knit. We measured the mass and dimensions of the fabrics. We also accurately measure the position of the two top corners using a Vicon motion capture system. We compute the projection matrices for the camera and projector using a calibration grid comprising of several motion capture markers. We performed two trials per experiment, each with slightly different initial conditions and optimized on the first 50 frames of video in each trial. Each trial took approximately 50 hours to converge on a 2.8GHz Intel Xeon processor (approximately 600 iterations of simulated annealing). For this reason, we started the optimizations on the two trials (per fabric) with the same initial guess and chose parameters (optimized) that minimized the total error on the two trials. Static test. We perform optimization on two trials for each fabric; the results are shown in Fig. 8 and Fig. 9 . The two trials have different separation distances between the top corners. For each fabric, we optimize for six parameters: stiffness and damping parameters for stretch, shear, and bend. The air drag parameters were fixed for this experiment to the mid point of their range of values. The initial values for the two trials are obtained from a coarse exhaustive search (four values per parameter). The initial values and final values of the estimated parameters are summarized in Table 1 . Figs. 8 and 9 show a very good visual match between the simulations with their counterpart real fabrics. However, there is a significant disparity in the final optimized values from the two trials. In order to understand this disparity, we performed a set of optimizations (on a single fabric) with very similar initial values. Table 2 shows the parameter values for satin from five optimizations where the initial conditions were randomly varied by ±5%. From the table, we see that the final error values are very close. We get consistent estimates for parameters that have lower variability (e.g., bend, stretch). Parameters with high variability are estimated poorly, because their values do not contribute sufficiently to the error. This result is consistent with our intuition that static tests cannot be used to estimate dynamic parameters like stretch and shear damping or air drag and motivates the waving test, which excites both the static and waving parameters. Waving test. We optimize for nine parameters in the waving test: the six cloth stiffness and damping parameters and three air drag parameters ( Fig. 10 ). As with the static test, we initialize the static parameters in this test from a coarse exhaustive search. The dynamic parameters were initialized using a random guess. We optimized on the first 50 frames of the sequence. The initial values and final values of the optimized parameters for two trials are reported in Table 3 . The final values of the parameters from the two trials differ in part because the variability of the parameters is still fairly high ( Fig. 11 ). Different motions or larger sequence might further reduce the variability of the parameters. We choose the parameter set that minimizes the sum of the error from the two trials. For instance, in the following example of fleece waving, we choose the parameters from experiment 2. Error: Exp 1 Error: Exp 2 Total Error Pars: Exp 1 4257.2 10913.5 15170.7 Pars: Exp 2 4566.2 7144.3 11710.5 This approach seems to produce plausible results with skirts and other validation experiments. However, we believe that a more general solution for parameter identification using our framework is to simultaneously optimize across multiple trials of different experiments. Optimization progress. Fig. 12 shows the static shape of the simulation before and after optimization. Fig. 13 shows the corresponding angle map comparison. These two figures show the progress of the optimization and indicate that the minimum corresponds to a visually compelling match. Metric validation. We compare each of the four optimized angle maps from simulation (corresponding to the four fabrics) with the four angle maps computed from video. In Fig. 14 , each curve shows one fabric (e.g., fleece) compared with four simulations, corresponding to each fabric type. We see that each fabric in simulation has a minimum error when compared to its counterpart in reality. Fig. 14 also demonstrates that our approach could be potentially useful for recognizing different types of fabrics in video. Generalization. We evaluated the parameters obtained from optimization on longer sequences (150 frames). Fig. 10 and the accompanying videos show a good visual match between corresponding frames in simulation and video. All videos are available off our web page and/or included in the DVD. The videos also show that the parameters obtained from optimization generalize well on new sequences. We also validated the estimated parameters on a long sequence actuated by a robot ( Fig. 15 ). We used a a Mitsubishi PA-10 robot arm to move the corner point along a simple sinusoidal trajectory, thereby ensuring that we had the same input motion across different fabrics. Finally, we used the optimized parameters to simulate a skipping motion of a human actor wearing a skirt ( Fig. 16 ). Here, the actor repeats the same skipping motion (approximately) for the four different skirts. We used data from a full body optical motion capture of the actor performing the same skipping motion (in another trial) to drive the character for the cloth simulation. The results show that the parameters obtained from our optimization approach approximately capture the static shape and dynamic properties of skirts of different materials.
        c The Eurographics Association 2003.
        Bhat et al. / Estimating Cloth Simulation Parameters from Video
        
          
          Figure 8: Results of optimization for the static test, trial 1. Top row: real fabrics (left to right) linen, fleece, satin and knit. Bottom row: Corresponding fabrics in simulation.
        
        
          
          Figure 9: Results of optimization for the static test, trial 2. Top row: real fabrics. Bottom row: Corresponding fabrics in simulation.
        
        
          
             Linen Fleece Satin Knit
            
              
                
                   Pars
                   Start
                   Exp 1
                   Exp2
                   Start
                   Exp 1
                   Exp 2
                   Start
                   Exp 1
                   Exp 2
                   Start
                   Exp 1
                   Exp 2
                
              
              
                
                   1
                   1e-3
                   0.009
                   0.0045
                   1e-4
                   0.0001
                   0.0001
                   1e-5
                   1.106e-5
                   6.94e-6
                   1e-6
                   1.52e-6
                   1.51e-6
                
                
                   2
                   4000
                   404.9
                   3682.1
                   50
                   129.2
                   200.04
                   50
                   19.58
                   19.38
                   50
                   27.97
                   28.36
                
                
                   3
                   215.442
                   175.374
                   208.15
                   215.442
                   103.96
                   31.391
                   50
                   76.81
                   69.65
                   50
                   1226.44
                   2693.07
                
                
                   4
                   1e-7
                   9.92e-7
                   3.22e-7
                   2.15e-6
                   2.13e-7
                   4.11e-7
                   1e-7
                   2.49e-7
                   3.98e-7
                   1e-7
                   1.01e-7
                   2.27e-7
                
                
                   5
                   10
                   12.16
                   10.17
                   10
                   4.78
                   0.064
                   10
                   14.42
                   3.68
                   10
                   10.12
                   11.83
                
                
                   6
                   10
                   2.19
                   13.17
                   10
                   13.86
                   3.75
                   10
                   4.11
                   4.56
                   10
                   0.13
                   4.04
                
              
            
          
          Linen Fleece Satin Knit Pars Start Exp 1 Exp2 Start Exp 1 Exp 2 Start Exp 1 Exp 2 Start Exp 1 Exp 2 1 1e-3 0.009 0.0045 1e-4 0.0001 0.0001 1e-5 1.106e-5 6.94e-6 1e-6 1.52e-6 1.51e-6 2 4000 404.9 3682.1 50 129.2 200.04 50 19.58 19.38 50 27.97 28.36 3 215.442 175.374 208.15 215.442 103.96 31.391 50 76.81 69.65 50 1226.44 2693.07 4 1e-7 9.92e-7 3.22e-7 2.15e-6 2.13e-7 4.11e-7 1e-7 2.49e-7 3.98e-7 1e-7 1.01e-7 2.27e-7 5 10 12.16 10.17 10 4.78 0.064 10 14.42 3.68 10 10.12 11.83 6 10 2.19 13.17 10 13.86 3.75 10 4.11 4.56 10 0.13 4.04
          Table 1: Tabulation of the static parameters from two experiments. Legend: 1=bend, 2=stretch, 3=shear, 4=bend damping, 5=stretch damping, 6=shear damping.
        
        c The Eurographics Association 2003.
        Bhat et al. / Estimating Cloth Simulation Parameters from Video
        
          
          
          Figure 10: Waving results for satin. The top picture in each block shows the real fabric and the bottom shows the corresponding frame from simulation.
        
        
          
          
        
        c The Eurographics Association 2003.
        Bhat et al. / Estimating Cloth Simulation Parameters from Video
        Bend Stretch Shear Initial Values 1.0e-05 50 50 Optimization 1 6.93766e-06 19.3832 69.653 Optimization 2 7.77204e-06 20.2884 32.6492 Optimization 3 8.75613e-06 19.8365 50.8304 Optimization 4 9.55647e-06 19.2745 74.7429 Optimization 5 8.47762e-06 20.1119 36.762 Variability (in %) 9.18 8.10 23.01
        
          Table 2: Performance of simulated annealing on several optimizations. All the optimizations start with values which are within ±5% of the initial values given in the first row. Parameters with high variability (e.g., stretch damping) are estimated poorly and vary significantly across the different optimizations. However, parameters with low variability (e.g., bend) are consistent across multiple optimizations.
          
             Linen Fleece Satin Knit
            
              
                
                   Pars
                   Start
                   Exp 1
                   Exp2
                   Start
                   Exp 1
                   Exp 2
                   Start
                   Exp 1
                   Exp 2
                   Start
                   Exp 1
                   Exp 2
                
              
              
                
                   1
                   1e-3
                   0.001
                   0.0008
                   1e-4
                   1.13e-5
                   0.0001
                   1e-5
                   6.41e-6
                   5.64e-6
                   1e-6
                   1.12e-6
                   1.16e-6
                
                
                   2
                   4000
                   2016.8
                   2935.26
                   50
                   82.61
                   89.32
                   50
                   26.42
                   32.37
                   50
                   69.75
                   12.68
                
                
                   3
                   215.442
                   167.833
                   465.73
                   215.443
                   255.198
                   296.861
                   50
                   97.77
                   74.24
                   50
                   37.48
                   59.99
                
                
                   4
                   1e-7
                   3.17e-7
                   4.76e-7
                   2.15e-6
                   1.36e-6
                   1.31e-6
                   1e-7
                   1.48e-6
                   1.24e-7
                   1e-7
                   1.04e-7
                   5.4e-7
                
                
                   5
                   10
                   2.71
                   5.17
                   10
                   2.39
                   5.92
                   10
                   0.57
                   4.48
                   10
                   4.52
                   3.87
                
                
                   6
                   10
                   3.89
                   5.52
                   10
                   1.59
                   9.82
                   10
                   6.57
                   4.73
                   10
                   4.93
                   2.64
                
                
                   7
                   2
                   8.73
                   2.18
                   2
                   2.40
                   1.62
                   2
                   4.85
                   0.85
                   2
                   1.54
                   0.99
                
                
                   8
                   2
                   5.56
                   1.99
                   2
                   3.15
                   0.31
                   2
                   1.76
                   1.48
                   2
                   0.52
                   1.79
                
                
                   9
                   2
                   0.44
                   1.29
                   2
                   4.28
                   1.23
                   2
                   0.95
                   0.79
                   2
                   1.22
                   0.33
                
              
            
          
          Linen Fleece Satin Knit Pars Start Exp 1 Exp2 Start Exp 1 Exp 2 Start Exp 1 Exp 2 Start Exp 1 Exp 2 1 1e-3 0.001 0.0008 1e-4 1.13e-5 0.0001 1e-5 6.41e-6 5.64e-6 1e-6 1.12e-6 1.16e-6 2 4000 2016.8 2935.26 50 82.61 89.32 50 26.42 32.37 50 69.75 12.68 3 215.442 167.833 465.73 215.443 255.198 296.861 50 97.77 74.24 50 37.48 59.99 4 1e-7 3.17e-7 4.76e-7 2.15e-6 1.36e-6 1.31e-6 1e-7 1.48e-6 1.24e-7 1e-7 1.04e-7 5.4e-7 5 10 2.71 5.17 10 2.39 5.92 10 0.57 4.48 10 4.52 3.87 6 10 3.89 5.52 10 1.59 9.82 10 6.57 4.73 10 4.93 2.64 7 2 8.73 2.18 2 2.40 1.62 2 4.85 0.85 2 1.54 0.99 8 2 5.56 1.99 2 3.15 0.31 2 1.76 1.48 2 0.52 1.79 9 2 0.44 1.29 2 4.28 1.23 2 0.95 0.79 2 1.22 0.33
        
        
          Table 3: Waving parameters from two experiments. Parameters from the experiment shown in bold is selected as the final estimate from this experiment. Legend: 1=bend, 2=stretch, 3=shear, 4=bend damping, 5=stretch damping, 6=shear damping, 7=linear drag, 8=quadratic drag, 9=drag degradation.
          
            
              
              
                
                   50
                  
                   50
                  
                
                
                   45
                  
                   45
                  
                
                
                   40
                  
                   40
                  
                
                
                   35
                  
                   Variability 35
                  
                
                
                   Variability 30
                  
                   30
                  
                
                
                   25
                  
                   25
                  
                
                
                   20
                  
                   20
                  
                
                
                   15
                  
                   15
                  
                
                
                   10
                  
                   10
                  
                
                
                   5
                  
                   5
                  
                
                
                   0
                  
                   0
                  
                
                
                   1 2 3
                   4 5 6 7 8 9
                   1 2 3
                   4 5 6 7 8 9
                
                
                  
                   Parameters
                  
                   Parameters
                
              
            
          
          50 50 45 45 40 40 35 35 Variability 25 30 Variability 25 30 20 20 15 15 10 10 5 5 0 0 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 Parameters Parameters
        
        
          Figure 11: Bar charts showing the variability analysis results for the waving test. From left to right: linen, fleece, satin and knit. Legend: 1=bend, 2=stretch, 3=shear, 4=bend damping, 5=stretch damping, 6=shear damping, 7=linear drag, 8=quadratic drag, 9=drag degradation.
        
        Bend Damp Stretch Damp Shear Damp Error 2e-07 10 10 179.026 3.98337e-07 3.67932 4.56238 104.747 2.08755e-07 1.95807 10.6535 104.502 2.56854e-07 7.08276 9.25576 103.501 3.14821e-07 5.47909 1.06559 103.243 2.3997e-07 8.38981 11.9167 103.849 21.11 &gt;100 &gt;100
        50 50 45 45 40 40 35 35 30 30 Variability 25 Variability 25 20 20 15 15 10 10 5 5 0 0 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 Parameters Parameters
        c The Eurographics Association 2003.
        Bhat et al. / Estimating Cloth Simulation Parameters from Video
        
          
          Figure 12: Showing the improvement in shape match after optimization. The top row compares a video frame of fleece with simulation before optimization. The bottom row shows the corresponding video/simulation pair after optimization.
        
        
          
          
          
          Figure 13: Comparison of angle maps for the shapes shown in Fig. 12 before and after optimization. Top Row (Before Optimization, from left to right): Angle map from video, angle map from simulation, angle map SSD. Bottom Row: The corresponding anglemaps after optimization.
        
        c The Eurographics Association 2003.
        Bhat et al. / Estimating Cloth Simulation Parameters from Video
        Linen Fleece Error 1 Satin Knit 2 Linen Sim Satin Sim Fleece Sim Knit Sim Optimized Simulation Parameters
        
          Figure 14: Comparing the optimized parameters in simulation for each fabric with the four real fabrics. For example, point 1 in the graph shows the error when a simulation with fleece parameters is compared with video of satin. Similarly, point 2 is the error when the satin simulation is compared with real satin. The four curves have a minimum when they are compared to their correct counterparts.
        
      
      
        