摘要
以三维模型为处理对象的数字几何处理技术正在快速发展,这使得三维模型检索成为研究的热点。特征提取是三维模型检索的关键技术,特征的优劣直接决定检索的效果。同时,输入样本的多元化极大地方便了用户。
本文以国家自然科学基金项目“融合三维统计形变结构的光学分子断层成像稀疏重建方法(编号：61372046)”为背景,在深入研究分析三维模型特征提取方法研究现状以及现有三维模型检索平台的基础上,综合运用微分几何、小波分析和数字图形图像处理等方法,研究以三维模型和二维图像为输入样本的三维模型检索问题。从多个角度提取出三维模型特征,如局部细节特征、整体距离特征、轮廓重心整体约束特征等,将多特征融合并应用于三维模型检索。同时,研究了图像变形方法,以提高基于二维图像的三维模型检索效率。
本文的主要工作如下：
(1)提出对局部特征的球函数进行调和分析的三维模型检索方法。三维模型面片顶点的平均曲率是函数的二次微分,表达了三维模型的细节信息。利用三维模型表面特征点的空间位置(θ，φ)与平均曲率(H)构造函数关系(θ,φ,H),通过对此函数进行球面调和分析得到模型的一组旋转、平移、缩放不变的新的局部特征,实现三维模型检索。
(2)提出对全局特征和局部特征进行特征融合的三维模型检索方法。利用整体特征,即模型表面特征点到其重心的距离对新的局部特征进行加权,得到一组新的特征向量,用于三维模型检索。新特征包含了三维模型局部与整体两方面的信息。使用新特征对三维模型库进行检索,实验结果表明新特征在查全率与查准率方面均优于单独使用整体或局部特征。
(3)提出二维图像轮廓重心整体约束特征描述子及其提取方法。针对以二维图像或手绘图为输入样本,采用改进场力优化的GVF-Snake模型与射线法联合提取出二维图像中的物体轮廓,提高了物体轮廓的提取准确度；为使三维模型特征库中三维模型的二维轮廓包含更丰富的信息,采用深度缓存投影的方法对三维模型进行二维图像轮廓提取；提出使用轮廓重心距离对轮廓线树形描述子进行加权,使轮廓线的相对位置得以限制,再融合轮廓线显著度,用以提高轮廓的辨识度,即可得轮廓重心整体约束特征描述子；最后,将得到的二维图像轮廓重心整体约束特征描述子和二维轮廓的Fourier特征描述子相融合进行三维模型检索。实验结果表明,融合空域和频域特征的二维轮廓描述子较之Fourier特征描述子有更高的查全率与查准率。
(4)提出基于点的小波滤波移动最小二乘(Moving Least Squares, MLS)图像变形方法。针对基于二维图像轮廓的三维模型检索,使检索者已有的二维图像或手绘图通过变形更接近于理想三维模型的二维图像,以提高三维模型检索效率。改变以往直接对图像进行变形的做法,首先对图像进行小波滤波,分成高频子图像和低频子图像,二者分别为原图像的细节信息与轮廓信息。轮廓的改变直接影响到基于二维轮廓特征的提取,故只对低频子图像进行MLS变形,高频子图像不作处理,这样则很好地保持了原图像的细节信息。再把变形后的轮廓信息与细节信息相加,得到最终的变形图像。实验表明这种方法操作简单,便于检索者表达出理想图像,使图像产生平滑和具有真实感的变形效果。
(5)提出基于控制曲线的小波滤波移动最小二乘图像变形方法。由于控制曲线比控制点有更好的控制能力和使图像变形更加平滑的能力,从而对基于控制点的图像变形进行了改进。小波滤波后,根据原图像的轮廓信息或在需要变形的地方设置关键点,使其生成控制曲线,把控制曲线移动到目标位置；然后,利用MLS方法实现图像变形。最后,再把变形后的轮廓信息与细节信息相加,生成最终的变形图像。所给方法较好地描述了轮廓信息,使变形成功率得到了提高。因为滤除了大量不需要变形的点,所以变形速度相应也得到了很大的提高。此方法也可以应用于一般领域的图像变形。
Digital geometry processing which takes3D model as the process object is rapidly developing. This phenomenon has made3D model retrieval become a research focus. What's more, feature extraction is a key technology in the process of the3D model retrieval and the retrieval result is directly determined by the quality of the features. Meanwhile, the diversity of input samples has brought great convenience to users.
Under the support of National Natural Science Foundation Project "Sparse reconstruction method for optical molecular tomography combing a three-dimension statistical deformable model"(Granted No.61372046), based on the research status of the development on the extraction of3D model feature as well as existing3D model retrieval platforms, by synthetically utilizing differential geometry, wavelet analysis and digital image processing method and so on, this thesis researches on3D models retrieval which uses3D models and two-dimensional images as input samples.3D model features are extracted in many ways, such as local detail features, entire distance features and entire constraint feature of contour barycenter and so on. The result of the multi-feature fusion is applied to the3D model retrieval. Meanwhile, the image deformation method has been researched to improve the efficiency of the3D model retrieval based on two-dimensional images. The main work completed in the thesis is listed as follows:
(1) A3D model retrieval method based on harmonic analysis of spherical function with local features is proposed. The mean curvature of3D model facet vertex is quadratic differential of function, which expresses3D model's detail information. The thesis structures a function which uses the spatial position and the mean curvature of the3D model surface feature point. The new local features of the model with the characteristic of no changing in rotation, translation and zoom is obtained by spherical harmonic analysis of the function.
(2) A3D model retrieval method based on the fusion of local and entire features is proposed. The entire feature which is the distance from the surface points to the model barycenter is used to weight new local feature and a group of feature vectors is gained. The new features contain both local and entire information of the3D model. The new feature is used to retrieve models in the3D model database and the experimental results show that the use of new feature the recall ratio and precision ratio are higher than the single use of entire or local feature.
(3) The entire restraint feature extraction method of the two-dimensional image contour barycenter is proposed. Aiming at input samples of the two-dimensional image or hand-drawing image, the object contour in the two-dimensional image is extracted by using combination of the improved field force optimize GVF-Snake model and ray method which improves the accuracy of object contour extraction; In order to make the3D model's two-dimensional contour in3D model feature database contain extensive information, the depth buffer projection method is adopted to extract the two-dimensional image contour of3D model; the contour barycenter distance is used to weight the contour tree descriptor, so that the relative position of the contour can be restricted. Moreover, fused with contour significant degree to improve the recognition of the contour, then the contour barycenter constraint feature descriptor is obtained. Finally, the overall constraint feature descriptor of two-dimensional image contours barycenter and feature descriptor Fourier of the two-dimensional contours to retrieve3D models is fused. The experimental results show that using the integration of spatial and frequency domain characteristics of the two-dimensional contour descriptor have higher recall ratio and precision ratio than using Fourier feature descriptor.
(4) An image deformation method based on wavelet filter using moving least squares (Moving Least Squares, MLS) is proposed. According to3D model retrieval based on two-dimensional image contour, the existing two-dimensional image or hand-drawing image of users can be closer to the two-dimensional images of ideal3D model by deformation. By improving the old ways which deform the image directly, this method can filter the original image into a high and a low frequency sub-image with wavelet which can better describe the detail and contour information respectively. As contour changes affect the extraction based on two-dimensional contour feature directly, so the low frequency image is deformed by MLS and the high-frequency sub-image isn't processed which can keep the detail information effectively. The final deformation image will appear by adding the deformed contour information to the details. The experimental results show that this method can be operated easily and it is easy for user to express ideal image, therefore the deformation results are satisfactory and realistic.
(5) An image deformation method based on wavelet filter using control curves and moving least squares is proposed. As the control curve has better control ability as well as better capacity in smoothing image deformation than control point, so the image deformation based on control points is improved. After wavelet filtering, according to contour information of original image or setting the key points in the needed deformation place, control curves can be generated and moved to target position to realize the deforming of image by using moving least squares. At last, the final deformation image can be obtained by adding the detail information to the contour information after deformation. This method can improve the success rate of the deformation by well describing the contour information. Because of having filtered out a great quantity of unnecessary deformation points, this method not only can improve the deformation peed greatly, but also can be applied to image deformation in general field.
引文
本章的相关工作己发表于2013年《Journal of Computational Information Systems》(EI期刊)。
本章的相关工作已发表于2013年《Journal of Information and Computational Science》(EI期刊)
本章的相关工作已发表于2013年《小型微型计算机系统》和2014年《Journal of Telecommunication, Computing, Electronics and Control》(EI期刊)
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