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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.
The symmetric 3-kernel [t/2, 1-t, t/2], for t ≤ 0.5 smooths to a scale of t using a pair of real zeros at Z < 0, and approaches the discrete Gaussian in the limit of small t. In fact, with infinitesimal t , either this two-zero filter or the two-pole filter with poles at Z = t /2 and Z = 2/ t can be used as the infinitesimal generator for the ...
For one-dimensional signals, there exists quite a well-developed theory for continuous and discrete kernels that guarantee that new local extrema or zero-crossings cannot be created by a convolution operation. [1] For continuous signals, it holds that all scale-space kernels can be decomposed into the following sets of primitive smoothing kernels:
The resulting image is larger than the original, and preserves all the original detail, but has (possibly undesirable) jaggedness. The diagonal lines of the "W", for example, now show the "stairway" shape characteristic of nearest-neighbor interpolation. Other scaling methods below are better at preserving smooth contours in the image.
An image scaled with nearest-neighbor scaling (left) and 2×SaI scaling (right) In computer graphics and digital imaging, image scaling refers to the resizing of a digital image. In video technology, the magnification of digital material is known as upscaling or resolution enhancement.
Visual representation of an image pyramid with 5 levels. Pyramid, or pyramid representation, is a type of multi-scale signal representation developed by the computer vision, image processing and signal processing communities, in which a signal or an image is subject to repeated smoothing and subsampling.
In image processing, ridge detection is the attempt, ... (1996, 1998) [5] coined the term scale-space ridge, he considered three measures of ridge strength:
Once established, the axioms narrow the possible scale-space representations to a smaller class, typically with only a few free parameters. A set of standard scale space axioms, discussed below, leads to the linear Gaussian scale-space, which is the most common type of scale space used in image processing and computer vision.
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