The effect of tendons on foot skin deformation

Abstract

Anatomical human models are usually divided into layers including skin, muscle and skeleton. In spite of the realistic animation of the models that can be achieved, and the realistic appearance of the model determined by the underlying muscles and skeleton, the role of tendons in determining the deformation of skin surface has not been well addressed.

This paper presents an approach for modeling human foot tendons and determines their influence on the skin layer deformation. Our goal is to model deformation of the tendons such that a realistic foot simulation can be obtained. An anatomical foot model including skin, muscle, tendon and skeleton layers is adopted. The appearance of the skin layer is determined based on the underlying layers. To allow interactive deformation of the tendon models, the axial deformation technique is adopted. Given the position of the foot and the basis function, the position of the data points that control the axial curve is updated. To allow more accurate computation of the data point positions, a method that estimates the basis function based on real data obtained from foot images is also presented. Experimental results showed that the axial deformation technique can model deformation of the foot tendons with satisfactory visual realism. With the tendon deformation, the visual realism on the skin deformation is also enhanced.

Introduction

Since the early 1970s, simulation of humans, and other animals has been one of the most important and interesting areas for researchers in CAD and computer graphics. However, due to the complexity of simulating the human body and its behavior, generating a realistic human model remains a difficult task.

To generate realistic human models or create animations, a direct approach is applying deformation on the skin surface of the characters. An accurate deformation of the skin layer can be modeled using physically based approaches including the finite element method (FEM). Recently, the development of more accurate modeling of the skin layer of human characters in computer graphics is based on their anatomical structure. The appearance of the skin is determined by the underlying muscles and skeleton layers. Although a substantial amount of work has been devoted to anatomically based modeling, deformation of the skin surface due to the underlying tendons has not been well addressed. Actually, the tendons play an important role in determining the skin surface deformation, especially on the foot and hand. For instances, the big toe pushing against the floor brings the tendon of the big toe into view (Fig. 1(a)) and the tendons appear on the surface of the hand when the fingers are extended (Fig. 1(b)).

Modeling tendon deformation is difficult because tendons may lie across several bone segments or have a large change in the direction of the line of action. One approach is to update the position of the tendon models by determining the movement of the corresponding action lines during motion. Modeling tendon motion according to muscle action lines is simple and easy to implement. However, the complicated motion of the tendon is largely simplified to move along a line segment. Besides, it is difficult to model the deformation of tendons lying across more than one skeleton joint. In this paper, a different approach for modeling tendon deformation is presented. The approach makes use of an axial curve which describes the deformation of tendon models. The complicated shapes of tendons are defined by the axial curve and used to control the deformation of the tendons during motion. A set of data points is used to define the shape of the axial curve. We present the tendon deformation on a human foot model. Our objective is to model deformation of the tendons such that a realistic human foot model can be simulated. The method is capable of achieving interactive deformation.

The tendon deformation technique is presented on a human foot model because:

• Foot tendons are one of the major underlying anatomical structures of the foot. They influence the appearance of the skin surface of the foot prominently;

• The foot contains many complex tendons to be modeled. The tendons may lie across several bone segments or have large changes in the direction of the line of action;

• Simulating foot tendon deformation has potential applications in shoe design. Fig. 2 shows a comparison of the foot model with and without tendons on wearing a slipper. The foot model with tendons has a larger contact region with the slipper. The simulation is useful for comfort analysis of shoes; and

• The technique for foot tendon deformation can be applied to other tendon deformation problems.

Over the past two decades, a great deals of effort has been focused on simulating human models [1]. However, it remains a great challenge in computer graphics because of the complexity of the human body and the animation of deformable skin layer of human characters requires geometric models changing over time. Free Form Deformation (FFD) introduced by Sederberg and Parry [2] provides flexibility for the users to control deformations of models. Barr [3] introduced the geometric method for modeling deformation of complex models. Although these methods provide flexibility for the users to control deformation, the realism of model deformation depends on the skill of the users rather than the intrinsic or physical properties of the models. In addition, the method is highly labour intensive and requires considerable skill in creating a realistic model. An accurate model of the skin layer of a character can also be obtained using physically based approaches such as FEM. Gourret et al. [4] simulate human skin deformation in a grasping task using FEM. The FEM is also applied to modeling the deformation of the underlying soft tissues or human organs [5], [6] and muscles [7], [8].

Recently, more accurate simulation of human characters has been developed based on their anatomical structure [9], [10], [11], [12], [13], [14], [15], [16], [17], [18], [19]. The technique divides the character models into layers including skin, fatty tissue, muscle and skeleton. According to the motions of the characters, the skeleton is transformed and the muscles are deformed accordingly. The appearance of the skin layer is determined by applying deformation on the multi-layered models [9]. Chadwick [10] proposed a methodology for creating and animating layered characters. Muscles are deformed using a simple geometric modeling technique and are used to determine the resulting geometric surface of the character. Scheepers [11] introduced an anatomy-based approach for modeling human musculation. Wilhelms [12], [13] developed a muscle model based on a simple deformable cylinder. The skin is generated by voxelizing the underlying muscles, bones and tissues, which is deformed during joint motions. Nedel and Thalmann [14] proposed to create a multi-layered human model. The muscle layer is deformed based on physical concepts. Kähler et al. [15] presented and constructed a muscle model to animate facial expressions. The muscle model is simplified as a quadratic shape. The mass–spring system is applied to simulate the fatty subcutaneous layer and control deformation of the skin layer. Albrecht et al. [16] constructed and animated an anatomically based human hand model by employing pseudo-muscles that compute the finger movements based on anatomical data and mechanical laws. The geometric muscles deform the skin tissue using a mass–spring system. Physics-based facial animation techniques are proposed in [17], [18]. An anatomy-based approach for face modeling is presented in [19]. Skeletal subspace deformation (SSD) [20] is a common approach used in surface deformation for character animation. Nevertheless, the method may not produce the desired results in regions around complicated joints and the range of motion is restricted. Kry [21] addressed these problems by using eigendisplacements and improved the results. Lewis et al. [22] proposed the pose space deformation (PSD) technique for skeleton driven deformation. Despite the large amount of research on simulating character models, the role of tendons in determining deformation of the skin surface has not been well addressed.

Dong and Clapworthy [23] presented an anatomy-based approach for human modeling based on the simulation of muscles. They attempt to simulate realistic muscle deformations by transforming the muscles according to the action lines. A cubic curve is used to fit the action line that consists of several line segments. The positions of the tendon models are updated by maintaining their angles with the action lines. Although the role of tendon models has been considered and updated according to the action lines, a detailed discussion on tendon deformations (e.g. bending of the tendons) and the corresponding deformation of the skin layer has not been presented. The method of tendon deformation presented in this paper attempts to tackle this problem.

The remainder of this paper is organized as follows. In Section 2 we identify the anatomical structures of the foot and discuss the tendon anatomy. In Section 3 we describe our method for modeling foot tendons. A technique that computes the basis function based on foot images is described in Section 4. We present the experimental results for modeling foot tendon and skin deformation in Section 5. Section 6 concludes the paper.