Dynamic Shape Modeling for Shape Changes

Probing the dynamic evolution of material structures, in response to physical or chemical stimuli, is of great interest to material scientists for the purpose of studying and designing novel materials. Studies of the dynamic evolutions are enabled through analyzing a sequence of microscopic images taken at different times or different stages of the evolutions. The time-resolved imaging can be acquired using in situ material imaging techniques, reviewed in Sect. 2.1 , or using ex situ material imaging when in situ imaging is not available. Here, ex situ imaging implies that a small quantity of sample material is taken for each intended measurement time and an offline imaging technique is subsequently applied. It provides an inexpensive and simpler alternative to in situ imaging, but in situ imaging does require a significant amount of time and efforts to manually take and prepare the samples for imaging. These in situ or ex situ images can be analyzed using different approaches, through either distribution tracking or object tracking. As explained in Chap. 7 , distribution tracking is concerned with discerning how a population of material objects collectively change over time, while object tracking is interested in knowing how material objects evolve individually or through mutual interactions. Chapter 7 presents the distribution tracking methods but for size change only. This chapter extends the discussion of distribution tracking for modeling shape changes or for both size and shape changes. The content of this chapter is based on the mathematical concept of shapes introduced in Chap. 4 , so reading this chapter requires a certain degree of understanding of Chap. 4 .