In this paper we show that a classic optical flow technique by Nagel and Enkelmann (1986, IEEE Tr... more In this paper we show that a classic optical flow technique by Nagel and Enkelmann (1986, IEEE Trans. Pattern Anal. Mach. Intell., Vol. 8, pp. 565–593) can be regarded as an early anisotropic diffusion method with a diffusion tensor. We introduce three improvements into the model formulation that (i) avoid inconsistencies caused by centering the brightness term and the smoothness term in different images, (ii) use a linear scale-space focusing strategy from coarse to fine scales for avoiding convergence to physically irrelevant local minima, and (iii) create an energy functional that is invariant under linear brightness changes. Applying a gradient descent method to the resulting energy functional leads to a system of diffusion–reaction equations. We prove that this system has a unique solution under realistic assumptions on the initial data, and we present an efficient linear implicit numerical scheme in detail. Our method creates flow fields with 100 % density over the entire image domain, it is robust under a large range of parameter variations, and it can recover displacement fields that are far beyond the typical one-pixel limits which are characteristic for many differential methods for determining optical flow. We show that it performs better than the optical flow methods with 100 % density that are evaluated by Barron et al. (1994, Int. J. Comput. Vision, Vol. 12, pp. 43–47). Our software is available from the Internet.
Image-processing transforms must satisfy a list of formal requirements. We discuss these requirem... more Image-processing transforms must satisfy a list of formal requirements. We discuss these requirements and classify them into three categories: “architectural requirements” like locality, recursivity and causality in the scale space, “stability requirements” like the comparison principle and “morphological requirements”, which correspond to shape-preserving properties (rotation invariance, scale invariance, etc.). A complete classification is given of all image multiscale transforms satisfying these requirements. This classification yields a characterization of all classical models and includes new ones, which all are partial differential equations. The new models we introduce have more invariance properties than all the previously known models and in particular have a projection invariance essential for shape recognition. Numerical experiments are presented and compared. The same method is applied to the multiscale analysis of movies. By introducing a property of Galilean invariance, we find a single multiscale morphological model for movie analysis.
In this paper we show that a classic optical flow technique by Nagel and Enkelmann (1986, IEEE Tr... more In this paper we show that a classic optical flow technique by Nagel and Enkelmann (1986, IEEE Trans. Pattern Anal. Mach. Intell., Vol. 8, pp. 565–593) can be regarded as an early anisotropic diffusion method with a diffusion tensor. We introduce three improvements into the model formulation that (i) avoid inconsistencies caused by centering the brightness term and the smoothness term in different images, (ii) use a linear scale-space focusing strategy from coarse to fine scales for avoiding convergence to physically irrelevant local minima, and (iii) create an energy functional that is invariant under linear brightness changes. Applying a gradient descent method to the resulting energy functional leads to a system of diffusion–reaction equations. We prove that this system has a unique solution under realistic assumptions on the initial data, and we present an efficient linear implicit numerical scheme in detail. Our method creates flow fields with 100 % density over the entire image domain, it is robust under a large range of parameter variations, and it can recover displacement fields that are far beyond the typical one-pixel limits which are characteristic for many differential methods for determining optical flow. We show that it performs better than the optical flow methods with 100 % density that are evaluated by Barron et al. (1994, Int. J. Comput. Vision, Vol. 12, pp. 43–47). Our software is available from the Internet.
Image-processing transforms must satisfy a list of formal requirements. We discuss these requirem... more Image-processing transforms must satisfy a list of formal requirements. We discuss these requirements and classify them into three categories: “architectural requirements” like locality, recursivity and causality in the scale space, “stability requirements” like the comparison principle and “morphological requirements”, which correspond to shape-preserving properties (rotation invariance, scale invariance, etc.). A complete classification is given of all image multiscale transforms satisfying these requirements. This classification yields a characterization of all classical models and includes new ones, which all are partial differential equations. The new models we introduce have more invariance properties than all the previously known models and in particular have a projection invariance essential for shape recognition. Numerical experiments are presented and compared. The same method is applied to the multiscale analysis of movies. By introducing a property of Galilean invariance, we find a single multiscale morphological model for movie analysis.
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Papers by Luis Alvarez