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Introduction
Volume deformation for computer graphics has been studied extensively over the past decade. Researchers have resorted to the FEM techniques for deformation of regular and unstructured geometrical objects. The issues are:

Large Voxel Data: Very little work has been done in the deformation of large voxel buffers. The enormous CPU and memory requirement to compute the FEM for voxels makes it not suitable for computer animation.
Voxel Deformation: Capturing large inelastic/plastic deformation of voxel objects using existing FEM systems and inverse kinematics for operations such as clapping of hands, involves the herculean task of specifying the constraints, the loads and the material for each voxel.
Goal-directed voxel deformations: In animating a voxel volume, the task is known. The voxel-human should walk, lift his hand or grasp an object. The only known entity is the goal or operation that needs to be performed. Translating this into appropriate forces, and constraints for each voxel is not an easy task.

Motivation:
     The two factors that motivated us to carry this work are:
         1. deformation of 3D geometry can be easily achieved using FEM models
         2. deformation of 2D textures can be used to achieve special effects.

To exploit the above two qualities for voxel-volume deformation, we first cluster a group of voxels to form larger blocks, transform the larger cells and then map the 3D textures into the deformed blocks. However, there is no work that has been reported for goal-directed FEM deformation. Also there has not been any work that has been reported so far for 3D voxel texture deformation of points, lines or polyhedrons.

Our Contribution
A new algorithm for goal-directed deformation of volume data is proposed. This method performs a clustering to identify voxels to form a polyhedron and deforms the polyhedron using FEM. The voxel textures for the deformed polyhedron are obtained using the voxture map algorithm. The attractive feature of the algorithm is that it is length, area and volume coherent and models a single volume texture from one or more 3D textures.

Voxture Mapping is defined as the process of assigning 3D volume texture to voxels during voxelization. In contrast to the texture lookup during the rasterization operation, which results in a texture-mapped frame buffer, the 3D volume texture sampling during voxelization results in a voxture-mapped volume buffer. A footprint is normally used to achieve the best approximation of the color of the resultant voxel.

Visible Human Deformation Algorithm
      This section describes the use of voxture mapping algorithm for deformation of a volume texture as shown in Figure 1. The steps involved are:
         1. Load the visible human as a single 3D texture.
         2. Discretize the visible human as 8-noded blocks.
         3. Deform the visible human blocks using FEM.
         4. Voxelize deformed blocks with Voxture Mapping.
         5. Render volume buffer.
         6. Repeat Step 3 for new deformations.

Results and Conclusion
An implementation of the new goal-directed deformation technique and results from visible human are presented. Figure 2 shows the results for the visible human data set. In contrast to the traditional deformation techniques, the new algorithm is aimed at volume transformations, deformations and volume metamorphosis. Work is in progress to deform the blocks using a multi-grid method where the bones and muscles have different deformation. We aim to achieve this by accumulating multiple voxture maps to obtain the deformed volume model.

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