International Journal of Digital Multimedia Broadcasting

Volume 2019, Article ID 6816453, 9 pages

https://doi.org/10.1155/2019/6816453

## Projection Analysis Optimization for Human Transition Motion Estimation

Department of Computer Science, Guangdong University of Education, Guangzhou, Guangdong 510303, China

Correspondence should be addressed to Wanyi Li; moc.361@2121rehtul

Received 7 November 2018; Revised 18 March 2019; Accepted 9 April 2019; Published 2 June 2019

Academic Editor: Jintao Wang

Copyright © 2019 Wanyi Li et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

It is a difficult task to estimate the human transition motion without the specialized software. The 3-dimensional (3D) human motion animation is widely used in video game, movie, and so on. When making the animation, human transition motion is necessary. If there is a method that can generate the transition motion, the making time will cost less and the working efficiency will be improved. Thus a new method called latent space optimization based on projection analysis (LSOPA) is proposed to estimate the human transition motion. LSOPA is carried out under the assistance of Gaussian process dynamical models (GPDM); it builds the object function to optimize the data in the low dimensional (LD) space, and the optimized data in LD space will be obtained to generate the human transition motion. The LSOPA can make the GPDM learn the high dimensional (HD) data to estimate the needed transition motion. The excellent performance of LSOPA will be tested by the experiments.

#### 1. Introduction

3-dimensional (3D) human motion animation is applied in many fields, such as video game and movie. It is necessary to estimate the human transition motion for making all kinds of 3D animations [1–4]. Estimating the human transition motion is crucial to making the smooth animation of the 3D human motion; it is a branch of human motion estimation. As to technologies of human motion estimation, there are some advanced methods in recent years, such as multiview image segmentation [5], sparse presentation [6], and convolutional neural network (CNN) coupled with a geometric prior [7]. These methods focus on the reconstruction of the 3D human motion from the 2-dimensional (2D) image sequence. The needed data is the high dimensional data of the 3D human motion model. The mapping will be built between the model and the 2D image for each frame. However, it is difficult to build the mapping without the overcomplete prior information, as a result of the data complexity during the optimization. Some human poses contain the ambiguity of limbs; for example, it is hard to determine which thigh is in the front from the silhouette. The right thigh or left thigh cannot be confirmed. The problem is that if we have enough prior information to distinguish the ambiguity, the reconstruction will be achieved easily. Thus the generated model of 3D human motion is necessary; the samples of the model can be obtained to construct the prior information. Besides, the generated model can also generate the 3D human motion for making 3D character movie. Then the generated model can be built through the unsupervised learning. The unsupervised learning of the model is the necessary supplement of the advantaged methods above. In this paper, how to generate the human transition motion will be mainly discussed in the following sections

If there is a method that can estimate the valid human transition motion, the animation making time will cost less, and the work will get easier. Thus a new method called latent space optimization based on projection analysis (LSOPA) is proposed to estimate the human transition motion. LSOPA needs to combine Gaussian process dynamical models (GPDM) [8] to process the low dimensional (LD) data. GPDM is the derivation of some dimension reduction models [9–13]; it can provide the prediction of the LD data. After the dimension reduction, LD data will be optimized by LSOPA, so that the valid human transition motion can be generated to achieve the estimation. The human motion is described by the high dimensional data. If the HD data sample is searched in its own dimensional space, the invalid data will be generated; it means the generated human motion in 3D will be abnormal [14]. GPDM is an unsupervised learning model; it can learn the high dimensional data (HD) sample and estimate the new one, but it needs to process the LD data in the LD space. In the LD space, the LD data can be searched, and the corresponding valid HD data can be generated by the mapping from LD data to HD data. Some methods [15–17] can process the LD data, but the generated LD data are all unreliable and undetermined during the optimization, as a result of the randomization of these methods. The LSOPA can do this work to process the LD data better and ensure the valid transition motion can be generated. The excellent performance of LSOPA will be tested by the experiments in the corresponding section.

The human motion is described by a 3D human motion model. The model has some markers to show the limbs of human motion; it is the HD data. When we make the 3D human motion animation and only have the samples of the two irrelevant human motions, it is necessary to use the transition motion to connect the two irrelevant human motions, so that the complete and smooth human motion in 3D is constructed. Meanwhile, the transition motion consists of many poses, and the poses are all the HD data samples of 3D human model, thus how to estimate the valid transition motion is a challenged task. However, the LSOPA can take the advantage of the GPDM to generate the valid transition motion and avoid generating the invalid pose of the transition motion. The proposed method will be discussed in the following sections.

#### 2. Dimension Reduction

When we have the sequence of HD data samples , the corresponding LD data can be obtained as the following equations from GPDM [8]:Equations (1)-(7) are used to computing (8), then the** X** and the other parameters can be got. In (1) and (2), we have the sequences , , respectively,** Y** denotes the HD data samples of 3D human motion, and** X** denotes the LD data of** Y** in the LD space after the dimension reduction. In (3) and (4), and are kernel matrices, respectively, and are their corresponding kernel parameters, and they satisfy the relation of (6) and (7), respectively. Equations (3) and (4) are showing the method of computing the two kernel matrices and . is a scale diagonal matrix with the preset parameter ,** x**_{1} conforms Gaussian distribution of dimensions, and is the sequence . The mapping from LD data to HD data can be built as follows:

The GPDM has a dynamic process. It can predict the LD data in the latent space (also called LD space) and generate the needed HD data of human motion, so that it has better performance than other dimension reduction models. Thus GPDM can be selected to learn the samples of the two different human motions; then the LD space can be built to find the needed LD data of the transition motion, so that corresponding poses can be generated through the mapping of (9).

#### 3. Latent Space Optimization Based on Projection Analysis

##### 3.1. The LD Data of the Transition Motion in the LD Space

After the dimension reduction, the HD data samples of the two irrelevant human motions can be seen in the LD space. The LD data of two difference sequences can denote the corresponding poses of the two irrelevant human motions. It can be found that there is an obvious distance between the two LD data as Figure 1 shows. From the two sets of LD data, we can know the needed transition motion can be generated through the LD space, but it needs to construct an appropriated curve to connect the two sets of LD data in the LD space. Thus, the optimized work will be started.