WebIn theoretical physics, the scaling dimension, or simply dimension, of a local operator in a quantum field theory characterizes the rescaling properties of the operator under spacetime dilations . If the quantum field theory is scale invariant, scaling dimensions of operators are fixed numbers, otherwise they are functions of the distance scale. Scale-space theory is a framework for multi-scale signal representation developed by the computer vision, image processing and signal processing communities with complementary motivations from physics and biological vision. It is a formal theory for handling image structures at different scales, by representing … See more The notion of scale space applies to signals of arbitrary numbers of variables. The most common case in the literature applies to two-dimensional images, which is what is presented here. For a given image See more Following the idea of expressing visual operations in terms of differential invariants computed at multiple scales using Gaussian … See more The theory presented so far describes a well-founded framework for representing image structures at multiple scales. In many cases it is, however, also necessary to select locally … See more There are interesting relations between scale-space representation and biological vision and hearing. Neurophysiological studies of biological vision have shown that there are See more The motivation for generating a scale-space representation of a given data set originates from the basic observation that real-world objects … See more At any scale in scale space, we can apply local derivative operators to the scale-space representation: $${\displaystyle L_{x^{m}y^{n}}(x,y;t)=\left(\partial _{x^{m}y^{n}}L\right)(x,y;t).}$$ Due to the … See more An image pyramid is a discrete representation in which a scale space is sampled in both space and scale. For scale invariance, the scale factors should be sampled exponentially, for example as integer powers of 2 or √2. When properly constructed, the … See more

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