You are presented with multiple paper abstracts, alongside the associated literature review and chapter titles. Given the provided information, you are going to do a literature review. Please generate a coherent literature review that synthesizes the content, draws connections between different works, highlights major findings, and identifies any gaps in the existing research.

Literature Review Title: A Survey on Non-rigid 3D Shape Analysis 
Chapter Title:  Metrics that capture physical deformations 
1. Abstract of Cited Paper (BIB001):  In this paper we define a new methodology for shape analysis of parameterized surfaces, where the main issues are: (1) choice of metric for shape comparisons and (2) invariance to reparameterization. We begin by defining a general elastic metric on the space of parameterized surfaces. The main advantages of this metric are twofold. First, it provides a natural interpretation of elastic shape deformations that are being quantified. Second, this metric is invariant under the action of the reparameterization group. We also introduce a novel representation of surfaces termed square root normal fields or SRNFs. This representation is convenient for shape analysis because, under this representation, a reduced version of the general elastic metric becomes the simple $\ensuremath{\mathbb{L}^2}$ metric. Thus, this transformation greatly simplifies the implementation of our framework. We validate our approach using multiple shape analysis examples for quadrilateral and spherical surfaces. We also compare the current results with those of Kurtek et al. [1]. We show that the proposed method results in more natural shape matchings, and furthermore, has some theoretical advantages over previous methods.

Literature Review:
Instead of using the L 2 metric on C f , one would like to explicitly capture the type of deformations that one needs to apply to f 1 in order to align it onto f 2 . Such deformations can be of two types; bending and stretching. This requires redefining Eqn. (5) in terms of an energy function that penalizes these deformations: where E s and E b are respectively the stretching and bending energies. The parameters α s and β s ∈ R + control the contribution of each of the terms to the energy function. Below we discuss two important pieces of work that implement this model. The first one (section 3.2.1) is inspired by the elasticity theory in physics BIB001 where surfaces are treated as thin shells, i.e. a thin three-dimensional material of thickness δ. Stretching in this case is caused by inlayer (tangential) shear or compression while bending is caused by friction due to transversal shear  . The second one (Section 3.2.2) showed that with specific choices of the bending and stretching terms as well as their weights, the deformation model of Eqn. (11) reduces to an L 2 metric in the space of Square Root Normal Fields (SRNF), a special representation of surfaces BIB002 .