Morphing 

        Morphing is the process of changing one figure into another. For example, the following is a morphing process, changing a cube into a sphere. 

  

 

 

 

        The process of morphing is not unique. If we parameterize it in order to match the direction well, it could have different effects. 

 

 

 

        Which one is better? It depends on how we judge a morphing effect. We hope that we can keep some features of the given surfaces during the morphing process. In this study, we propose some efficient ways to obtain the morphing effects that we want. 

 

 

   Mesh Denoising 

        The mesh data captured from the 3D camera is full of noise and holes. We may use the free software, "Meshlab", to cut-off the noise along the boundary and fill holes manually. But it costs much time. 

 

 

 

 

        In order to do it in a more efficient way, we may separate the mesh denoising problem into three steps: boundary smoothing, canonical boundary cut, and hole filling. 

 

 

 

    Conformal Morphing

         Suppose S1 and S2 are simple connected surfaces with a boundary in R3. We may use conformal map φ1:S1→ D1 and φ2:S2→ D2, where D1 and D2 are unit discs in R2 with center (0,0). We may simply pick a rotation γ:D1 → D2. Then f = φ2-1。γ。φ1 → S1 to S2

 

 

 

▲The conformal morphing process from a pillow into a doll with γ = rotation( 0° ).

 

 

▲The conformal morphing process from a pillow into a doll with γ = rotation( 90° ).

 

 

 

 

    Conformal Morphing with Beltrami Surface Reconstruction 

       The effect of morphing between two different facial expressions of a human face is not always fine, especially when the variation of boundaries of two patches is huge. In order to morph between different facial expressions of a human face well, some facial features must be kept during the morphing process. Under the assumption that the facial expressions are similar to another, we can keep the facial features matched using canonical boundary.

 

 

 

 

 

 

    Conformal Morphing with Matching Technique 

        The ratio of facial features differ from every person. In order to morph one's face into another well, in other words, keeping the facial features matched during the morphing process, matching of the feature points is important. 

      We may choose an appropriate matching function f: D1→D2 such that f matches their facial features well. Then f = φ2-1f。φ1$ maps S1 to S2 which preserves the continuity of facial features. 

 

 

 

 

 

        We may apply the conformal morphing with matching technique to make a series of motion picture with two pictures only. 

 

 

▲The morphing process from a girl's face into another.

 

 

▲The conformal morphing process from a bitter smile face into a pout emotion.

 

 

▲The conformal morphing process simulating the motion of eye blinking.

 

 

 

   3D Film Compression

         The 3D film, captured from our 3D camera, contains 30 mesh figures and the corresponding texture images per second. The file size of an original mesh figure captured from our 3D camera is about 30 megabytes. We may use merely about 10% of the original mesh frames to rebuild the whole film. 

 

 

                  

▲The real 90-frame chewing-gum motion picture (left) and the simulation with merely 10 frames (right).

 

 

 

    Video Compression 

 

This is the chewing-gum motion picture, simulating a motion of 750 pictures with 72 pictures (9.6%), using the conformal single mesh with matching technique. 

 

▲The real chewing-gum video.         ▲The chewing-gum motion picture.     ▲The mesh of the chewing-gum

                                                                                                                                motion picture.

 

 

 

 

    Virtual Brocasting 

 

 

 

The virtual broadcasting of 

登鸛雀樓: 白日依山盡,黃河入海流。欲窮千里目,更上一層樓。

 

 

 

 

    The digital acting

 

 ▲The chewing-gum motion picture   ▲The digital acting with 1 picture.    ▲The digital acting with 1 picture.

 simulating a 750-frame video with

 72 pictures.

 

 

 

 

 ▲The chewing-gum motion picture   ▲The digital acting with 1 picture.    ▲The digital acting with 1 picture.

 simulating a 750-frame video with

 72 pictures.

 

 

 

    Geodesic registration

This is the motion picture of facial expressions by using the conformal single mesh with geodesic surface registration. 

 

 

        

           ▲The motion picture with 8 facial expressions.          ▲The mesh of the motion picture.