**Scale Space**

**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 an image as a one-parameter family of smoothed images, the **scale-space representation**, parametrized by the size of the smoothing kernel used for suppressing fine-scale structures. The parameter in this family is referred to as the *scale parameter*, with the interpretation that image structures of spatial size smaller than about have largely been smoothed away in the scale-space level at scale .

The main type of scale space is the *linear (Gaussian) scale space*, which has wide applicability as well as the attractive property of being possible to derive from a small set of *scale-space axioms*. The corresponding scale-space framework encompasses a theory for Gaussian derivative operators, which can be used as a basis for expressing a large class of visual operations for computerized systems that process visual information. This framework also allows visual operations to be made *scale invariant*, which is necessary for dealing with the size variations that may occur in image data, because real-world objects may be of different sizes and in addition the distance between the object and the camera may be unknown and may vary depending on the circumstances.

Read more about Scale Space: Definition, Motivations, Gaussian Derivatives, Detector Examples, Scale Selection, Related Multi-scale Representations, Biological Vision, Implementation Issues, See Also

### Other articles related to "scale space, scale, scales":

... In image processing and computer vision, a

**scale space**framework can be used to represent an image as a family of gradually smoothed images ... This framework is very general and a variety of

**scale space**representations exist ... A typical approach for choosing a particular type of

**scale space**representation is to establish a set of

**scale**-space axioms, describing basic properties of the desired

**scale**-space representation and often ...

... A Gaussian

**scale space**representation of an image is the set of images that result from convolving a Gaussian kernel of various sizes with the original image ... A larger

**scale**, corresponds to a smoother resultant image ... that derivatives and other measurements must be normalized across

**scales**...

**Scale Space**- See Also

... Complementary articles on specific subtopics of scale space scale-space axioms scale space implementation scale-space segmentation multi-scale approaches Multi-scale feature detection within the scale-space framework edge detection blob detection corner detection ridge detection affine shape adaptation interest point detection The Gaussian function and other smoothing or multi-scale approaches Gaussian function Gaussian filter multi-scale approaches wavelets anisotropic diffusion nonlinear scale space smoothing pyramid (image processing) mipmapping More general articles on feature detection, computer vision and image processing feature detection (computer vision) computer vision image processing. ...

**Scale Space**Implementation

... The linear

**scale**-space representation of an N-dimensional continuous signal is obtained by convolving with an N-dimensional Gaussian kernel However, for implementation, this ... When applying the

**scale space**concept to a discrete signal, different approaches can be taken ...

... Koenderink proposed to study how iso-intensity contours evolve over

**scales**and this approach was investigated in more detail by Lifshitz and Pizer ... the intensity of image features changes over

**scales**, which implies that it is hard to trace coarse-

**scale**image features to finer

**scales**using iso-intensity information ... Lindeberg studied the problem of linking local extrema and saddle points over

**scales**, and proposed an image representation called the

**scale**-space primal sketch which makes explicit the ...

### Famous quotes containing the words space and/or scale:

“The within, all that inner *space* one never sees, the brain and the heart and other caverns where thought and feeling dance their sabbath.”

—Samuel Beckett (1906–1989)

“It is in vain that we would circumscribe the power of one half of our race, and that half by far the most important and influential. If they exert it not for good, they will for evil; if they advance not knowledge, they will perpetuate ignorance. Let women stand where they may in the *scale* of improvement, their position decides that of the race.”

—Frances Wright (1795–1852)