Higher order SVD analysis for dynamic texture synthesis
Higher order SVD analysis for dynamic texture synthesis
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DOI：
10.1109/tip.2007.910956
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发表时间：
2008-01-01
影响因子：
10.6
通讯作者：
Suesstrunk, Sabine
中科院分区：
文献类型：
--
作者：
Costantini, Roberto;Sbaiz, Luciano;Suesstrunk, Sabine
代表火焰、水、烟雾等的视频，通常被定义为动态纹理：“纹理”是因为它们的特征是图案的冗余重复，而“动态”是因为这种重复也是在时间上而不仅仅是在空间上。动态纹理已被建模为线性动态系统展开的视频帧到列向量，并描述其随时间演变的轨迹。在通过奇异值分解（SVD）将向量投影到低维空间上之后，使用系统识别技术对轨迹进行建模。通过用随机噪声驱动系统来获得合成。在本文中，我们表明，标准的SVD可以取代高阶SVD（HOSVD），最初被称为塔克分解。HOSVD将动态纹理分解为多维信号（张量），而无需将视频帧展开到列向量上。这是一种更自然和灵活的分解，因为它允许我们在空间，时间和色度域中执行降维，而标准SVD仅允许时间降维。我们表明，对于一个可比的合成质量，HOSVD方法需要，平均而言，五倍少的参数比标准的SVD方法。分析部分是更昂贵的，但合成具有相同的成本，现有的算法。我们的技术，因此，非常适合于动态纹理合成的内存和计算能力有限的设备，如PDA或移动的电话。
Videos representing flames, water, smoke, etc., are often defined as dynamic textures: "textures" because they are characterized by the redundant repetition of a pattern and "dynamic" because this repetition is also in time and not only in space. Dynamic textures have been modeled as linear dynamic systems by unfolding the video frames into column vectors and describing their trajectory as time evolves. After the projection of the vectors onto a lower dimensional space by a singular value decomposition (SVD), the trajectory is modeled using system identification techniques. Synthesis is obtained by driving the system with random noise. In this paper, we show that the standard SVD can be replaced by a higher order SVD (HOSVD), originally known as Tucker decomposition. HOSVD decomposes the dynamic texture as a multidimensional signal (tensor) without unfolding the video frames on column vectors. This is a more natural and flexible decomposition, since it permits us to perform dimension reduction in the spatial, temporal, and chromatic domain, while standard SVD allows for temporal reduction only. We show that for a comparable synthesis quality, the HOSVD approach requires, on average, five times less parameters than the standard SVD approach. The analysis part is more expensive, but the synthesis has the same cost as existing algorithms. Our technique is, thus, well suited to dynamic texture synthesis on devices limited by memory and computational power, such as PDAs or mobile phones.