本文選題：數(shù)字幾何處理　切入點(diǎn)：形狀插值　出處：《華南理工大學(xué)》2016年博士論文　論文類型：學(xué)位論文

【摘要】：基于網(wǎng)格的動(dòng)態(tài)幾何序列生成與壓縮是計(jì)算機(jī)動(dòng)畫的理論基礎(chǔ).幾何序列的生成方式主要有掃描儀獲取、基于關(guān)鍵幀的形狀插值、基于物理驅(qū)動(dòng)的變形、對已有幾何序列進(jìn)行編輯與操縱等.形狀插值因其交互少、控制簡易以及效果直觀,成為動(dòng)畫設(shè)計(jì)常用的幾何序列生成技術(shù).通過對已有幾何序列進(jìn)行編輯與操縱,動(dòng)畫設(shè)計(jì)師能更加靈活地獲得更豐富的、更具個(gè)性化的動(dòng)態(tài)幾何序列.另一方面,生成的原始幾何序列往往占用大量存儲空間,需要壓縮技術(shù)對其進(jìn)行高效存儲.基于視覺誤差的壓縮方法在近年備受關(guān)注.本文對基于三維網(wǎng)格的形狀插值、序列編輯、序列姿態(tài)移植以及序列壓縮等內(nèi)容進(jìn)行了研究.本文提出一種快速擬等距三維網(wǎng)格插值技術(shù),將形狀插值問題表示為尋找三角形邊向量的擬等距路徑的非線性問題,并建立相關(guān)數(shù)學(xué)模型.求解非線性問題的初始化階段,提出一種基于邊正交標(biāo)架及連結(jié)映射的傳播-優(yōu)化算法,能有效、快速地解決大尺度變形插值問題;在迭代優(yōu)化階段,采用塊坐標(biāo)下降法,將序列的全體未知量優(yōu)化解耦為逐條邊的優(yōu)化,并進(jìn)一步簡化后者的求解,顯著降低計(jì)算復(fù)雜度.對于序列編輯與姿態(tài)移植,通過操縱每一幀鄰接頂點(diǎn)的相對速度以達(dá)到修改序列模型姿態(tài)的目的.最后,提出一個(gè)適用于形狀插值、序列編輯以及序列姿態(tài)移植的統(tǒng)一計(jì)算框架.實(shí)驗(yàn)表明,相比目前最好的形狀插值技術(shù),擬等距形狀插值算法能夠獲得更加符合等距約束的序列,而且更加高效.本文提出一種新的同構(gòu)網(wǎng)格序列的壓縮算法.注意到對齊序列中的姿態(tài)會(huì)增加信息冗余度,本算法分析由網(wǎng)格序列所構(gòu)成的頂點(diǎn)軌跡矩陣,通過剛性變換對齊序列模型,尋找軌跡子空間,使軌跡的線性相關(guān)性盡可能大.首先,算法對整個(gè)序列進(jìn)行運(yùn)動(dòng)分析并分割網(wǎng)格模型的剛性塊,然后對頂點(diǎn)軌跡矩陣進(jìn)行低秩分解,用以引導(dǎo)剛性塊對齊,并采用主成份分析表示剛性塊對齊后的軌跡.剛性變換、主成分分析的基與其混合系數(shù)使用現(xiàn)有動(dòng)態(tài)網(wǎng)格壓縮技術(shù)保存.實(shí)驗(yàn)結(jié)果表明,在相同的視覺誤差條件下,本算法的性能與目前最好的壓縮方法相當(dāng);如果序列的運(yùn)動(dòng)接近分塊剛性,本方法具有較大的壓縮優(yōu)勢.
[Abstract]:Generation and compression of dynamic geometric sequences based on mesh is the theoretical basis of computer animation. Geometric sequences are generated by scanners, shape interpolation based on key frames, and deformation based on physical drive. Shape interpolation has become the common geometric sequence generation technology in animation design because of its less interaction, simple control and visual effect. By editing and manipulating the existing geometric sequence, the shape interpolation has been used in animation design. Animation designers are more flexible in getting richer, more personalized dynamic geometric sequences. On the other hand, the original geometric sequences often take up a lot of storage space. The compression method based on visual error has attracted much attention in recent years. In this paper, shape interpolation based on 3D mesh, sequence editing, In this paper, a fast quasi-equidistant three-dimensional mesh interpolation technique is proposed, in which the shape interpolation problem is expressed as the nonlinear problem of finding the quasi-equidistant path of the triangular edge vector. At the initialization stage of solving nonlinear problem, a propagation-optimization algorithm based on edge orthogonal frame and link mapping is proposed, which can effectively and quickly solve the large-scale deformation interpolation problem. By using the block coordinate descent method, the optimization of all unknown variables of the sequence is decoupled to the edge-by-side optimization, and the solution of the latter is further simplified, and the computational complexity is significantly reduced. By manipulating the relative velocity of the adjacent vertices of each frame to modify the posture of the sequence model, a unified computing framework suitable for shape interpolation, sequence editing and sequence attitude transplantation is proposed. Compared with the best shape interpolation technique at present, the pseudo-equidistant shape interpolation algorithm can obtain the sequence which is more consistent with the equidistant constraint. In this paper, a new compression algorithm for isomorphic mesh sequences is proposed. It is noted that the pose of alignment sequences increases the redundancy of information. The algorithm analyzes the vertex locus matrix composed of mesh sequences. The linear correlation of the trajectory is as large as possible by aligning the sequence model with the rigid transformation. Firstly, the algorithm analyzes the motion of the whole sequence and segments the rigid block of the mesh model. Then the vertex locus matrix is decomposed in low rank to guide the alignment of rigid blocks, and principal component analysis (PCA) is used to express the trajectory after alignment. The basis of principal component analysis and its mixing coefficients are preserved by existing dynamic mesh compression techniques. The experimental results show that the performance of this algorithm is comparable to that of the best compression method under the same visual error conditions. If the motion of the sequence is close to block rigidity, this method has a large compression advantage.
【學(xué)位授予單位】：華南理工大學(xué)
【學(xué)位級別】：博士
【學(xué)位授予年份】：2016
【分類號】：TP391.7

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