Differences between image, volume, and surface

Image Data is a 2-dimensional matrix, P = f (x, y)
Even volume data is a three-dimensional matrix, P = f (x, y, z)
Mesh is a set of triangles and polygon. It is used to represent the surface.

Image enhancement is usually implemented by modifying the color and intensity. In fact, the data of the image is directly modified.
Mesh enhancement is usually implemented by modifying the vertex positions of these elements (triangles, etc.) and normal.
The volume enhancement is usually implemented by modifying the transparency to obtain a new opacity * volume data. Therefore, all operations must be combined with opacity.

In volume data, raw data of scalar values usually has only one value. To understand the feature in volume
Directly perform the transfer function on this value and the value derived from this value, and adjust the opacity to make the unwanted parts invisible.
The lighting transfer functions using gradient aligned sampling of Erick Lum actually introduces this value to light,
In the past, light was used to set just a few coefficients, and he established the relationship between this coefficient and the value.

In this year's shape-aware volume statement, Wei Chen split the volume data to generate several surfaces, which are processed by triangular mesh or others, then, use some mesh processing methods to enhance the surface so that the final image and shape are highlighted. In fact, there is no big difference between combining silhouettes, shading, and volume rendering for surgery Education and Planning and hardware-acclerated stipping of surfaces derived form mediacal volume data in Christian tietjen05, the latter uses line and point to express the shape of the separated surface, while the former performs some operations on the mesh of the surface.

Why can we get the surface after division? Arie Kaufman in http://www.cs.sunysb.edu /~ Vislab/projects/volume/papers/index.html #10. volume data lacks geometric information. currently, the transfer function does not take this into account. Although spatialized transfer functions uses the spatial histogram to take the position into account in the transfer function, it is a global histogram for the surface local detail, the effect is not obvious.
Of course, it is difficult for researchers to integrate it directly into the transfer function.

How can we solve these problems? How can we directly obtain the geometric information of surface elements from volume, such as triangular mesh and line?