<H1>3 Analyzing Acquisition Methods</H1>
        To acquire a 3D point cloud of the cloth surface, we print a colored pattern on the cloth, sew it together, and record its motion using multiple synchronized cameras. We then reconstruct the 3D location of surface points by detecting corresponding points in multiple views ( figure 4 ). Our goal is high marker density in the 3D reconstruction – especially in regions with high curvature. To achieve this, we need markers that are both small in scale and highly discriminative. These two goals are in tension: small markers are less discriminative. In addition, we cannot increase camera resolution without bound because camera bandwidth becomes very expensive. As a result, we opt for the smallest markers that we can reliably detect and we make small markers more distinctive. We combine information from three cues to establish correspondence: marker color, neighboring markers and strain constraints in the reconstruction. Marker color and strain constraints are more useful than neighboring markers because they place fewer requirements on local cloth geometry. Specifically, neighboring markers are observed only when the cloth is relatively flat. When the surface is heavily curved only small portions of the surface are visible before the cloth curves out of view. In subsequent sections we adopt the following strategy: maximize information obtained from marker color and eliminate the information needed from neighbors.
        parametric domain
        
          <H2>3.1 Entropy as an Analytical Tool</H2>
          We optimize our correspondence technique by analyzing the information provided by different cues. In this framework we can accurately minimize the number of neighbors required for correspondence and observe folds better. We can compare our work to previous methods using this framework ( figure 6 ). It takes log 2 M bits to determine the identity of each observed marker on a garment with M total markers. Because independent information adds linearly, we can compute the information needed to meet this threshold by adding information from the different cues: color, neighbors and strain. However, structural ambiguities in the pattern subtract information lost to determine which neighbor is which. As a result, we compute our information budget (I ) as:
          N = number of observed neighbors C = color information per marker A = information lost to structural ambiguities S = information gained from strain constraints I = (N + 1) ∗C + S − A
          As an example, imagine a rectangular grid of markers and a correspondence method that uses a single immediate neighbor. This neighbor is one of four possible neighbors – thus it takes two bits to specify which neighbor we found (A = 2). In this case, the equation reduces to I = 2 ∗C − 2 + S. Given almost any structured pattern, we can detect regions by increasing N until I &gt; log 2 (M) bits. However, larger marker regions have the disadvantage that curvature can cause local occlusions and prevent observation of the entire region. Our best efforts are to improve C – the number of bits from each marker observation. We do this by picking marker color from the full colorspace instead of a small discrete set of colors.
          
            
            
          
        
        
          <H2>3.2 Garment Design and Color Processing</H2>
          We print a random colored pattern on the surface of cloth in an attempt to maximize the information available per pixel. While our pattern is composed of tesselated triangles ( figure 5 ), any shape that tiles the plane will work (squares and hexagons are also natural choices). To maximize the density of reconstructed points, we print the smallest markers that we can reliably detect. To maximize the information contained in the color of each marker, we print colors that span the gamut of the printer-camera response, then use a gaussian color model (section 4.1). From a system view, the printer-camera response is a sequence of lossy steps: we generate a color image on a computer, send the image to the printer, pose the cloth, and capture it with a camera. Our experiments suggest that loss is largely attributable to camera response because larger markers produced substantially more information. Illumination is also problematic and takes two forms: direct illumination on a lambertian surface and indirect illumination. To correct for variations in direct illumination, we remove the luminosity component from our color modelling. We do not correct for indirect illumination. Each marker in the printed pattern has a randomly chosen color, subject to the constraint that neighboring marker colors must be dissimilar. In the recognition stage, we detect markers by comparing colors to a known color. These comparisons must be made in the proper color space: we photograph the surface of the printed cloth with our video cameras to minimize the effect of non-linearities in the printing process.
        
      
      
        