IEEE TRANSACTIONS ON VISUALIZATION AND COMPUTER GRAPHICS 1 The Squash-and-Stretch Stylization for Character Motions Ji-yong Kwon, In-Kwon Lee Abstract—The squash-and-stretch describes the rigidity of the character. This effect is the most important technique in traditional cartoon animation. In this paper, we introduce a method that applies the squash-and-stretch effect to character motion. Our method exaggerates the motion by sequentially applying the spatial exaggeration technique and the temporal exaggeration technique. The spatial exaggeration technique globally deforms the pose in order to make the squashed or stretched pose by modeling it as a covariance matrix of joint positions. Then, the temporal exaggeration technique computes a time-warping function for each joint, and applies it to the position of the joint allowing the character to stretch its links appropriately. The motion stylized by our method is a sequence of squashed and stretched poses with stretching limbs. By performing a user survey, we prove that the motion created using our method is similar to that used in 2D cartoon animation and is funnier than the original motion for human observers who are familiar with 2D cartoon animation. Index Terms—Squash-and-stretch, Cartoon stylization, Motion capture, Exaggeration, Covariance matrix, Time warping ✦ 1 I NTRODUCTION R ESEARCHERS have developed a wide variety of novel methods to generate realistic character mo- tion. These methods, such as physically based ap- proaches or data-driven motion synthesis, can easily generate realistic human motion data. Nevertheless, this realistic motion cannot be used directly in 3D car- toon animation. Most cartoon animations still depend on hand-made keyframe motion, which requires labor- intensive manipulation by skillful animators. Further- more, a novice user cannot make a quality keyframe animation, because quality keyframe animations require experience with and talent in this technique. Most of the early methods for motion synthesis are based on modeling and depicting the real world (i.e., usage of equations of motion, new motion synthesis from thousands of motion capture data sequences). However, characters in cartoon animation move according to the rules of the cartoon world, which are quite different from those of the real world. In cartoon animation, characters may stretch to reach a target quickly, squash due to a sudden stop or move, and deform their bodies to express feeling. These cartoon-stylized motions suitably portray the expression of the character and attract the audience. Although the rules of the cartoon world depend on the intention of the animation director, ‘The Illusion of Life’ [1] is one of the most important reference guides for understanding the rules of cartoon animation. This book introduces the principles of traditional cartoon animation created by Walt Disney. Additionally, Lasseter [2] explained how to apply these rules to 3D cartoon • J. Kwon and I. K. Lee are with the Department of Computer Science, Yonsei University, Korea. E-mail: mage@cs.yonsei.ac.kr animation. As stated in the literature, the most important technique in cartoon animation is “Squash-and-Stretch”, which describes the rigidity of objects by squashing and stretching them. Except for a few rigid objects, most objects in traditional cartoon animation follow this rule and exaggerate their characteristics around the rigidity. Characters that have bones also adhere to this rule. This paper introduces a method that automatically enhances the squash-and-stretch effect for a given real- istic motion, such as motion capture data. After careful observation and a review of the animation literature, we formulate the squash-and-stretch rule using two types of optimization: spatial and temporal optimization. The motion stylized by our method is not only funny, but also similar to several examples in traditional cartoon animation. The rest of the paper is structured as follows. In Sec- tion 2, we review previous work related to our method. Our review of the animation literature, key features and a brief overview of our method are presented in Section 3. The details of our method are described in Sections 4 and 5. Section 6 presents and discusses results produced by our method, and Section 7 discusses the quality of our results from the user survey. The last section of the paper presents our conclusions. 2 RELATED WORK We focus on non-realistic motion, although there are many techniques for creating realistic motion that are not clearly related to our work. Although the need for non-photorealistic animation has been understood only relatively recently, several ways of generating exaggerated or attenuated motion have already been proposed, which are mostly based on signal processing techniques. Unuma et al. [3] addressed