- Research
- Open Access

# Seamless images stitching for 3D human models

- Chao Lai
^{1, 2}Email author, - Fangzhao Li
^{1, 2}and - Shiyao Jin
^{1, 2}

**Received:**15 December 2015**Accepted:**29 September 2016**Published:**10 October 2016

## Abstract

Realistic 3D human model reconstruction is an important component in computer graphics and computer vision. In particular, texturing on the surface of models is a key stage of reconstruction. In this paper, we dispose the texture mapping on the model’s surface as an optimization of image stitching, and present an effective method to generate a seamless, integrated and smooth texture on the surface of 3D human model. First, we build a corresponding Markov Random Field model with respect to color images and triangular meshes of the surface. On the basis of \(\alpha\)-expansion optimization for this Markov Random Field model, a 2D translation coordinate of color image, as an adaptive iterative factor, is introduced into the optimization to match the color content at the boundary of adjacent meshes. That compensates for the misalignment of adjacent color images, which caused by the inaccuracy of depth data and multi-view misregistration. Then we apply Poisson blending to a composite vector field in gradient domain, to resolve the small but noticeable illumination variations between different color images. To repair the blank regions, we parameterize the model’s surface and project it onto a 2D plane. Then the K-Nearest Neighbor algorithm is applied to fill up the blank regions with texture contents. Finally, we evaluate our method by comparison with another three advanced methods on some human models, and the results demonstrate that our method of images stitching creates a best texture on the surface of 3D human model both in visual effect and quantitative analysis.

## Keywords

- Images stitching
- Adaptive iterative factor
- Smooth
- Seamless

## Background

Realistic 3D model reconstruction (Li et al. 2013) is an important component in computer graphics and computer vision, and comprehensively applied in our daily life, especially in films, animations, video games, virtual reality and so on. It is an underway revolution from 2D to 3D, which gradually makes the reconstruction of the real world come true. As an innovative technological application, 3D human reconstruction makes the humans get rid of the visual fatigue of 2D frames, and it opens a novel and fascinated domain to acquaint ourselves with the real world much more fascinating.

A high-quality texture on the surface of model is a key component of the reconstructed model, which impacts the visual effect significantly. In this paper, our goal is to generate a seamless texture on the surface of given 3D human model, from a set of images obtained by multiple RGB-Depth cameras.

In a large amount of previous works on this problem, they reconstruct an accurate 3D model and generate a preferable texture on the surface of model by using complex equipment, such as laser scanning and structured light. However, these methods require such an expensive and complex facility that can’t be used extensively.

The emergence of RGB-Depth cameras in recent years, such as Kinect produced by Microsoft and Xtion by Asus, paves the way to settle this matter. Evidently, it becomes widely applied due to its low price, simplified operation and hand-held shape, although the accuracy is not as high as the former.

Due to the limitation of accuracy of RGB-Depth camera, some dramatic misaligned seams are produced on the texture. But even using the facility of laser scanning and structured light, the inaccuracy of depth data and multi-view misregistration also result in these seams. Besides, some irrelevant contents of environment are mixed with the objective texture. In addition, the inaccuracy of depth data and multi-view misregistration result in some blank regions without any color contents, which destroy the integrity of texture. Furthermore, due to the different ray gains of cameras from respective directions, as well as surface reflection, the local variations in illumination is noticeable between color images, which damages the visual effect significantly and degrade the quality of texture.

In this paper, to eliminate these artifacts, we treat the texture mapping on model’s surface as an optimizaiton of images stitching, and propose a method of global optimization to compensate for the inaccuracy of depth data and multi-view misregistration. In our method, an extra adaptive iterative factor is introduced into the parameters of images stitching, and the texture images are allowed to move gradually to match the color content at the boundary of adjacent meshes. Finally, the misaligned seams are eliminated by iterative optimization.

Regarding irrelevant environmental contents, we build Gaussian Mixture Models (GMM) (Rother et al. 2004; Ruzon and Tomasi 2000; Chuang et al. 2001) in the color space, and segment the image into two parts, objective and environment. Therefore, only objective content remains in the images while the environmental contents are erased.

To solve the issue of illumination variations between adjacent color images, we construct a composite vector field in the gradient domain of color space, with the points located in the boundary as constraints. Due to the pixels distributing discretely, we solve the resulting discrete Poisson equation (Perez et al. 2003), and blend the adjacent color images smoothly. Thus the color of different images becomes coherent.

Last but not least, we parameterize the surface of model and project it onto a 2D plane. Then the K-Nearest Neighbor algorithm is applied to search for K points with color content, and the pixels in blank regions are filled with the average content of the K points. Then we back project the plane onto the surface, and all the blank regions become textured with color contents. Consequently, an integrated and consistent texture is generated on the surface of 3D human model, as shows in Fig. 6.

## Related work

It is a classic topic that creating a texture on the surface of objective model, and the key is to minimize the visible seams caused by multi-view misregistration and inaccuracy of data. Catmull (1974, 1980), begin to use the texture mapping skill to improve the visual quality of images generated by raster scanning facility. Rocchini et al. (1999) confirm the best texture for each triangular mesh by projecting the color images onto the surface of 3D model, and apply the region expansion algorithm to complete the ambient texture projection. It guarantees the validity of inner texture for local areas, but results in discontinuities in the boundary of images. Liu et al. (2006) resolve the discontinuities in the boundary effectively by global optimization of the multiple texture images using bundle adjustment. Zhou et al. (2005) implement coarse-to-fine strategy of several levels, considering both geometric and images in overlapping textures, and complete the textures montage.

Different from the previous work, it has become popular recently that projecting the model surface onto the color images and forming the texture as images stitching problem (Wang et al. 2001; Thormahlen and Seidel 2008; Dessein et al. 2014). It combines the images with triangular meshes as a Markov Random Field and constructs an objective energy function of cost. Despite the elegance and power of the energy minimization approach, the algorithms which were previously used, such as iterated conditional modes (ICM) (Besag 1993) and simulated annealing (SA) (Barnard 1989), proved to be ineffective. Boykov et al. (2001) present two algorithms based on graph cuts that effectively find a global minimum of the energy function. As is well known, it has been widely applied in a great amount of cases, such as stereo matching (Barnard 1989; Boykov et al. 2001), image segmentation (Rother et al. 2004; Boykov and Jolly 2001) and image denoising (Felzenszwalb and Huttenlocher 2006). Belief propagation (BP) (Felzenszwalb and Huttenlocher 2006; Yedidia et al. 2000; Tappen and Freeman 2003) is a powerful optimization algorithm to resolve the energy minimization and widely used in a large variety of tasks. Especially in stereo matching, it usually gets a dramatic result. However, BP is not guaranteed to converge and may go into an infinite loop switching between two labelings. If BP converges and there are no ties in the min-marginal for nodes, it often achieves the local minimum.

To eliminate the noticeable seams on the mosaic image, Lempitsky and Ivanov (2007) cast the problem of seams visibility minimization as an optimization of a mesh based Markov Random Field energy, and propose a seam leveling procedure to remove out the mosaic seams without affecting fine details of the texture. Without any move of the texture content, some distortions occur in the boundary of adjacent meshes, accompanied with some slight seams. Ran et al. (2010) present an automatic method to recover high-resolution texture over an object by mapping detailed photographs onto its surface, which minimizes the visible seams by applying the Tree-Reweighted Message Passing algorithm (TRW-s) (Vladimir 2006) to achieve a global minimization, and then assigns smooth texture to adjacent triangular meshes with a set of local image transformations. In practice, there is no guarantee that the energy might not actually increase with time, and the energy sometimes starts to oscillate.

Soler et al. (2002) present an approach to form a seamless texture over the surface meshes by optimizing a set of per-face image transformations in a greedy manner. Eisemann et al. (2008) pose the method of optical flow to handle with these noticeable seams, which calculates the pairwise warping between the images and then blended at the rendering stage. Dessein et al. (2014) present a method to blend the sampled images by least-angle selection of gradients in overlapping patches, but ignore nonlinearity due to specularity and shadows. Dessein et al. (2015) segment the faces into patches, and blend the sampled textures to synthesise a seamless texture over the surface.

Among these methods, it is a common feature that each mesh of the surface can be project onto at least one image. However, in practice, it is general that blank regions without any texture content exist on the surface of model, caused by inaccuracy of depth data and multi-view misregistration. In this paper, we present a method of parameterization of the surface, combined with K-Nearest Neighbor algorithm, to deal with these blank regions, and then fill up them with color contents to create an integrated and coherent texture on the surface of model.

Color fusion in gradient domain (Fattal et al. 2002; Chuang et al. 2009) has been widely applied in a large variety of tasks to produce a new smooth image from the original images. Levin et al. (2004) apply gradient domain fusion in stitching the panoramic mosaics together. Raskar et al. (2004) blend multiple images of a common scene with different illumination intensity in the gradient domain, and consequently generate surrealist images with much more information. Perez et al. (2003) introduce a method of Poisson image editing to blend images into a single image by copying the objective region of a single image into a destination image in the manner of gradient domain. In our work, we add the points in the boundary of adjacent images into the Poisson equation as constraint to make it over-constrained.

In this paper, we propose a method of creating a seamless texture mapping on the model’s surface with a rapid optimization. We introduce an adaptive iterative factor to expand the texture, and the texture is allowed to move towards to match with adjacent meshes at the shared edge. Then the \(\alpha\)-expansion algorithm is applied to handle the energy optimization in an iterative strategy. The results of experiments demonstrate the effectiveness of our method both in visual observation and qualitative analysis.

## Seamless images stitching

### Texture generation

To cover the objective model, We set up multiple RGB-Depth cameras around it. Then a set of color images and depth data are simultaneously generated by these cameras, which are used to calculate a texture mapping between meshes of the surface and pixels in the color images. With the point cloud of depth data, we first reconstruct the mesh of model’s surface by the method which we proposed in paper (Lai et al. 2015). First we do the registration of the point cloud by the iterative closest point (ICP) algorithm (Besl and Mckay 1992). Then we optimize the noisy raw data by bilateral filtering algorithm (Christian et al. 2012) and finally apply the Poisson surface reconstruction algorithm (Kazhdan et al. 2006) to create the mesh of model’s surface. With the set of color images and the reconstructed mesh of model’s surface, we seek to reconstruct the texture from the images by using a projective map from each triangular mesh to one of the images, as shown in Fig. 1.

*d*is the location in depth data,

*q*is depth value, \(\delta _d\) and \(\phi _d\) are the center and projection parameters of depth data. Then the coordinate of 3D point in global coordinate system is obtained,

*R*is a rotation matrix and

*T*is a translation vector. Therefore, the correspondent relationship between 3D points and pixels in the color images is established as follows,

### Images enhancement

*T*components (typically \(T = 5\)). Therefore, a vector \(t=\{t_1,\ldots ,t_n\},t_i\in \{1,\ldots ,T\}\), is formed to assign a unique GMM component to each pixel in the color image. For GMM components, we define \(a = 1\) for foreground and \(a = 0\) for background. Then the energy function for segmentation is introduced as follows,

*t*. So \(E_d\) is defined as follows,

*n*. Step 2, it is implemented as a set of Gaussian parameter estimation procedures as follows. For a given GMM component

*t*in the foreground model, the subset of pixels \(F(t) = \{p_n : t_n = t , a_n = 1\}\) is defined. The mean \(\mu (a,t)\) and covariance \(\Sigma (a,t)\) are estimated in standard fashion as the sample mean and covariance of pixel values in

*F*(

*t*), and the weights are \(\delta (a,t) = |F(t)| / \Sigma _t|F(t)|\), where |

*F*(

*t*)| denotes the size of

*F*(

*t*). Finally, step 3 is a global optimization, using minimum cut, exactly as this paper (Boykov and Jolly 2001). Repeat from step 1 until convergence.

### Seamless optimization

The filtered color images from these cameras, which covers part of model respectively, should be stitched together to create an integrated texture on the model’s surface. Due to the multi-view misregistration and inaccuracy of depth data, it produces some undesirable artifacts in the initial texture, such as misaligned seams at the boundary between different color images, illumination variation between different parts of the texture, and blank regions without any texture contents. These artifacts are small but noticeable, and degrade the visual quality significantly, as shows in Fig. 3.

#### Markov Random Field model

*x*for each triangular mesh, which identifies its best associated color image. Then we create the Markov Random Field model as the following form.

*I*. Then we get the best texture label for each triangular mesh, and project the corresponding color image onto the triangular mesh , from which it is visible.

In this Markov Random Field model, each node denotes a triangular mesh with a set of optional texture labels, and the solution of the optimization substantially assigns a best texture label, namely color image, to each triangular mesh of the surface.

#### Optimization with adaptive iterative factor

The \(\alpha\)-expansion algorithm is summarized as follows. Given an arbitrary initial labeling *f* and a label \(\alpha\), a weighted edge is formed between neighboring nodes, and the goal is to find a new labeling \(f'\) which minimizes the energy over all the nodes’ labels through one \(\alpha\)-expansion move. During the \(\alpha\)-expansion move, it just changes the nodes whose label is not \(\alpha\), and the other nodes whose label is \(\alpha\) maintain the same value. If the energy of new labeling \(f'\) is less than the original, it continues to perform another one \(\alpha\)-expansion move; otherwise, returns the current labeling \(f'\) with the minimal energy. Therefore, the returned labeling \(f'\) is the final solution of the energy function, which assigns a best label to each triangular mesh.

*x*as the form of \(x=(I_i,t)\), where \(I_i\in \{I_1,\ldots ,I_N\}\). Then, during the \(\alpha\)-expansion move, we can move the pixels in the color space of images adaptively and iteratively, to match the color content precisely at the edge shared by adjacent triangular meshes. As a result, the misalignment seams would be removed significantly. So the second term becomes this form

*e*(

*t*) is the unit coordinate vector.

In the optimization of seams, we treat each color image as an individual image space. After each triangular mesh of the model’s face is projected on the color image, the location of the mesh on the color image is obtained. Then, with the adaptive iterative factor, a 2D translation vector, the location of mesh is changed along the possible directions. Finally, we get the best location by comparing the color content of two adjacent triangular meshes at the shared edge. In the initialization of the optimization, every triangular mesh is assigned a set of possible labels, that means the mesh can be projected onto these color images, and the adaptive factor is set to be zero. Then we calculate the energy function iteratively to find the optimal labels, and move the texture image gradually, with a threshold of 32 pixel units, to match the color content at the shared edge of adjacent meshes. Therefore, the misaligned seams, caused by the inaccuracy of depth data and multi-view misregistration, are eliminated. In each cycle of iteration, each node is assigned the current best label by energy optimization. Furthermore, to confirm the assigned label *x* being the best label for node *i*, we fix the neighbor nodes with their assigned best label, and calculate the sum of energy of \(\sum V_{ij}(x_i^*,x_j)\) for all the possible labels of node *i*. If another label \(x'\) achieves the minimal energy, we abandon the assigned label *x* and choose the label \(x'\) as the best label for node *i*. As the iterative strategy is applied to the energy optimization, the result of current iteration is further fed into next iteration as candidate labels, until a best labeling \(f'\) achieves the global minimum of the energy optimization over all the nodes’ labels. Finally, the optimized texture without misalignment seams is obtained, as Fig. 4 shows.

### Color blending

Although these misaligned seams can be eliminated effectively by the optimization of MRF, one artifact of illumination variation in different images still remains, caused by the different ray gains of RGB-Depth cameras from respective positions, as well as the reflection of surface. This small but noticeable artifact significantly degrades the texture and visual effect.

*g*, the composite vector field as

*V*, and the boundary between adjacent color images as

*b*, where the pixels keep fixed as constraints for color blending. Accordingly, the objective function is

*I*(

*u*,

*v*). Then the divergence of vector field \(\vec {V}\) specifies two linear equations, each involves two variables,

### Blank region repair

After the illumination variations are handled effectively by the process of color blending, last remaining artifact is blank regions, which is caused by inaccuracy of depth data and multi-view registration. As there is no corresponding relationship between the meshes in these areas and color images, some blank regions without any texture content exist on the surface of model, which destroy the integrity of texture.

*K*neighboring points with color contents, and then create the texture image for blank regions with these color contents, shown in Fig. 6.

- (1)
Search for

*K*colored neighboring points of the blank point in the projected plane. While the number of colored neighboring points is less than*K*, the range of search extends to neighbors of these colored points until the number is equal or greater than*K*. - (2)
Calculate the distance respectively from the

*K*colored points to the blank point, and refer to the maximum among them as Dmax. Given another colored point with distance*D*, compare it with colored point of \(D_{max}\). If*D*is larger than \(D_{max}\), then abandon the former; otherwise, replace the latter with the former of value*D*, and then update the maximum distance among the new*K*colored points. - (3)
Repeat step 1 and 2, until the

*K*colored points no longer update.

## Implementation and results

Energy and runtime of optimization for various methods

Models | Measure item | BP | Mosaicing | Montage | Ours |
---|---|---|---|---|---|

Woman | Energy | 56,137,613 | 11,212,098 | 10,174,383 | 10,174,183 |

Runtime(s) | 104.64 | 10.68 | 1051.97 | 14.83 | |

Man | Energy | 64,274,859 | 13,793,729 | 14,706,724 | 11,474,016 |

Runtime(s) | 127.61 | 13.42 | 1166.19 | 20.16 | |

Doll | Energy | 346,328,438 | 8,148,734 | 7,633,248 | 7,633,137 |

Runtime(s) | 92.85 | 10.76 | 947.82 | 12.47 |

*x*axis shows the runtimes in seconds on a log scale and the

*y*axis shows the energy of the different methods over time, and the energy and runtime of minimization are shown in Table 1. The other three state-of-the-art methods we compared are Belief Propagation(BP), Mosaicing(using graph cuts), and Montage(using Tree-Reweighted Message Passing, namely TRW-s).

In the corresponding result of energy minimization (Fig. 9), the plot shows the energy of different methods over time and some interesting features. The BP algorithm just converges to a local minimum, far away from the global minimum, and the runtime is at the level of \(10^2\) s. The Mosaicing method finds a near-optimal solution most quickly at the level of \(10^1\) s. Although the energy of Montage gradually approaches to the global minimum, it takes a large amount of time at the level of \(10^3\) s. Furthermore, during the process of calculation, it does not decrease progressively but oscillates widely. That means, if it is used in limit time and iterative frequency, it would not achieve the global optimal. Our method achieves the global minimum by aligning the texture contents at the boundary between adjacent color images, and converges quickly and progressively at the level of \(10^1\) s, just slightly slower than the Mosaicing method.

Furthermore, to evaluate the effectiveness of our method, we implement these methods on the doll model, which is previously published in Mosaicing and Montage. As shown in Fig. 12, some noticeable seams and ghost artifacts are produced on the result of BP, as BP algorithm converges to a local minimum and could not align the adjacent meshes at their shared edge. Obviously, these undesirable artifacts seriously degrade the performance of BP. Although superior to the BP, the Mosaicing can’t eliminate the seams. Due to the error of multi-view registration and inaccuracy of depth data, the adjacent meshes can not match their color content at the shared edge without moving the texture image. Thus the seams and broken texture are still noticeable. In contrast, the Montage brings out a desirable texture in visual observation, without any seams and ghost artifacts. But it needs sufficient iterations to converge to the global minimum, which takes a lot of time. Otherwise, if the number of iteration is insufficient, the performance of Montage will severely decline, especially when it is in the oscillation, just as the result of the man model. Meanwhile, our method also provides a seamless texture. In the process of optimization, the misaligned textures are moved with the adaptive factor to match their color content at the shared edges, and the energy decreases progressively and converges straightforward to the global minimum without any oscillation. Thus, our method achieves the optimal result much faster than Montage, as listed in Table 1. Based on the experiments of our human models and the previously published doll model, the comparison indicates that our method is effective for reduction of seams, with a rapid optimization.

According to the experiments, we know that the BP algorithm may go into a region of local minimum and could not step out to converge to the global minimum, and some misaligned seams and distortions still remain at the shared edge of adjacent meshes through the Mosaicing algorithm. Although the Montage algorithm generates a favorable texture in visual observation without any seams, it needs abundant iterations and larger time expense to converge to the global minimum, especially accompanied with wide oscillations. In order to create a seamless texture on the model’s surface with a rapid optimization, we propose a method of introducing an iterative factor into the \(\alpha\)-expansion algorithm. As the \(\alpha\)-expansion algorithm is able to change the label of several nodes simultaneously, with such a large move, it is effective to get rid of the local minimum and converge rapidly to the global minimum during the optimization. Furthermore, with the iterative factor, the texture of mesh could be moved gradually to match the color contents at the shared edge of adjacent meshes, which compensates for the inaccuracy of depth data and multi-view misregistration. As the texture is aligned at the boundary, the energy of optimization decreases dramatically and converges straight towards the global minimum without any oscillation, leading to a large acceleration of optimization. However, the major limitation of our proposed method is model’s movement. That means, the person should keep motionless as a statue until the color image and depth data have been obtained by the cameras. If the person moves his or her body during the process, the movement will result in terrible damage to the corresponding relationship between color images and depth data, and the error of mismatch is so huge that our method could not handle effectively. In future work, we will take the slight movement of human body into consideration, which involves the nonrigid registration of human body.

## Conclusion

In this paper, we present an effective method to generate a seamless, integrated and smooth texture on the surface of 3D human models. Given a set of color images obtained by multiple RGB-Depth cameras around the human model, and a surface mesh reconstructed previously by point cloud, we establish a MRF model. To eliminate the seams at the boundary between adjacent color images, caused by multi-view misregistration and inaccuracy of depth data, we introduce an adaptive iterative factor into the MRF model. To smooth out the noticeable illumination variation between different color images, we apply the state-of-the-art method of Poisson blending to a composite vector field in gradient domain. Furthermore, we perform parameterization of the model’s surface and apply KNN algorithm to repair the blank regions without texture content. To evaluate the effectiveness and robustness of our method, we compare it with another three advanced methods. The results demonstrate that our method achieves the global minimum of optimization almost fastest and creates a best texture on the surface of models. Therefore, our method proves evidently effective and preferable both in visual effect and quantitative analysis.

## Declarations

### Authors’ contributions

Chao Lai carries out concept generation, designs the experiment for comparing four methods design, analyzes and interprets the result, composes and revises the manuscript draft. Fangzhao Li and Shiyao Jin carry out the concept generation, designs the experiment and revise the manuscript. All authors read and approved the final manuscript.

### Competing interests

The authors declare that they have no competing interests.

### Consent to publish

We have been approved to use and publish the human model in our manuscript under the permission of Chen Yin and Yang Yun.

**Open Access**This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

## Authors’ Affiliations

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