Blur

High definition
Image blur

The blur is a form of uncertainty, ambiguity or uncertainty in the figure or reproduction of an object or state of affairs. Blurring is not necessarily a mistake; in the case of blurring , for example, it is desirable, in quantum mechanics it is of a fundamental nature and therefore unavoidable.

Basics

Sharpness (as the opposite of blurring) is defined as the clear distinguishability of details (when reproducing an image or facts). Blurring is the lack of distinguishing features between original and image and is defined as an inaccuracy of an object or fact - always depending on the context of the observation. This yardstick - the context - determines a perception as "fuzzy".

• Example of blurring in the figure:
Depending on the evaluation standard, the photo on the left (contains less contrast) or the photo on the right (contains fewer details) is perceived as blurring.
• Example of blurring in the reproduction of a fact:
All birds fly with the help of their wings . This statement contains a certain degree of fuzziness, which is expressed in various possible interpretations:
1. Example: All birds can fly because they have wings. That statement would be wrong.
2. Example: When birds fly, they fly with the help of their wings. This statement is context dependent.

photography

The edge sharpness can be used as a measure of the sharpness of an optical image or an image . This describes a special criterion that can be observed on edges. Put simply: the more abrupt the transition from dark to light at an edge, the sharper the image. If the image brightness is plotted over the location, along a line perpendicular to the edge, then the edge sharpness is greater, the steeper the brightness curve at the transition from the dark to the light area increases. The exact course of this curve determines both the resolution and the microcontrast.

In photography, the term blurring is often used somewhat blurred: it can refer to the resolution or the brilliance. High resolution means that there is a lot of detail in the picture. High brilliance means that the difference in brightness between neighboring areas in the image, i.e. H. the contrast, is great; the details are reproduced more clearly. An image with low brilliance (such as the one on the left of the example images above) is sometimes perceived as blurred and described, although the resolution can be high.

The process known as "sharpening" in image processing is used to increase the microcontrast, so it makes an image appear sharper without increasing the resolution (missing detailed information cannot of course be "added" to the image afterwards). Microcontrast is understood to be the difference in brightness that occurs directly at an edge, i.e. H. the jump in brightness at the edge. A low micro-contrast arises from the fact that part of the light that comes from an object point is not focused on the image point, but is distributed in its immediate vicinity. Certain aberrations in the lens (especially spherical aberration ) can cause this. This does not necessarily degrade the resolution.

The possible causes of blurring in photography are:

The imaging errors of the lens can worsen the resolution and / or microcontrast, depending on the type of error. The other causes mentioned reduce the resolution.

A sharp image is created when each point of the object is mapped to a point on the image plane . If an image point is in front of or behind the image plane, a blurred image (defocusing) occurs. Stopping down increases the depth of field . Blurring due to the different course of marginal rays and rays that run through the center of the lens can be reduced by stopping down (reduction of aberrations). Blurring in photography sometimes acts like a limitation of the frequency spectrum of the spatial frequencies - this corresponds to a low-pass filter , so the high frequencies are removed.

Blurring can also be caused by:

• the contamination of the lenses of the lens
• The blurring of an entire image or part of an image, which is used for artistic purposes and is either created when taking a picture with a special lens or a blur attachment, or when editing the image with a filter of the Blur type .
• dull image reproduction, d. H. with too low a contrast; makes the picture look blurred, but without reducing the resolution

A certain amount of blurring are typical characteristics of photos:

• soft gradients between the colors
• Colored areas with natural structure
• Merging of different picture elements (without edges that look like “cut with scissors”).

physics

The "fuzziness" of a measurement result due to the lack of resolution of the measuring apparatus is usually referred to as uncertainty , as a distinction to the use of the term in quantum mechanics .

Signals and waves

A wave cannot be fixed to a place or time. If, for example, a water wave is to be measured more precisely, the height of the water level is determined at certain locations at different times. An infinite number of measurements are required for an exact description of a wave; in practice, only a finite number of measurements can be carried out. This leads to a blurring in the measurement of wave phenomena.

Amplitude of a signal with frequency as a function of time (above) and as a function of frequency (below).${\ displaystyle f_ {0} = {\ tfrac {\ omega _ {0}} {2 \ pi}} = 500 \, \ mathrm {Hz}}$${\ displaystyle t}$${\ displaystyle f = {\ tfrac {\ omega} {2 \ pi}}}$
Amplitude of a square pulse as a function of time (above) and frequency (below).${\ displaystyle t}$${\ displaystyle f = {\ tfrac {\ omega} {2 \ pi}}}$

A monochromatic wave is a wave with only one frequency . The wave is described by the deflection (for example the height of the water level) as a function of location and time . The direction and speed are also determined by the wave vector . The deflection is a consine function of the form ${\ displaystyle \ omega _ {0}}$${\ displaystyle A (x, t)}$${\ displaystyle x}$${\ displaystyle t}$ ${\ displaystyle k}$

${\ displaystyle A (x, t) = \ cos (\ omega _ {0} t-kx) \ ,,}$

Here, for the sake of simplicity, the units of measurement are chosen so that an amplitude of one and a phase of zero result. At a fixed point in time like there is no area in which the deflection is for constant zero. The same applies to a fixed location , i.e. a signal ${\ displaystyle t = 0}$${\ displaystyle x \ to \ pm \ infty}$${\ displaystyle t \ to \ pm \ infty}$${\ displaystyle x = 0}$

${\ displaystyle A (t) = \ cos (\ omega _ {0} t) \ ,.}$

Using Fourier transformation , the signal can also be described as a function of the frequency${\ displaystyle \ omega}$

${\ displaystyle {\ tilde {A}} (\ omega) = {\ frac {\ delta (\ omega - \ omega _ {0}) + \ delta (\ omega + \ omega _ {0})} {2} } \ ,.}$

The delta distribution is an infinitely high, infinitely narrow peak with an area of ​​one. The description in this frequency space has the same information, whereby the respective phases must also be considered for completeness. Likewise, a wave can be represented by Fourier transformation with respect to reciprocal space . Just as the signal is related to, there is a connection between and . and or and are called conjugated or complementary quantities. ${\ displaystyle \ delta}$${\ displaystyle \ omega _ {0}}$${\ displaystyle x}$${\ displaystyle A (t)}$${\ displaystyle {\ tilde {A}} (\ omega)}$${\ displaystyle A (x)}$${\ displaystyle {\ tilde {A}} (k)}$${\ displaystyle t}$${\ displaystyle \ omega}$${\ displaystyle x}$${\ displaystyle k}$

A wave that is limited in time and space is a wave packet . It can be written as the sum of monochromatic waves. As a rule of thumb, the wider or longer a signal is in the space or time period, the narrower it is in the reciprocal or frequency space. For example , the shorter a sine tone , the more difficult it is to assign the pitch to a frequency.

Quantum mechanics

In quantum mechanics , two measurable quantities ( complementary observables ) are referred to as fuzzy if they cannot be measured at the same time with any precision. The best known example is location and momentum of a particle. Here Heisenberg's uncertainty principle says that the product of position uncertainty and momentum uncertainty cannot be smaller than half Planck's constant of action . In contrast to the uncertainty in classical wave phenomena, this uncertainty is not caused by a finite number of measurements, but of a principle nature.

Logic and language theory

The classical logic is characterized by two sharp states: true and false ; the life experience , however, shows that these two truth values often are not enough. Fuzzy logic as fuzzy logic , however often lead to better results - especially if the templates vague or imprecise.
Theories of language based on the results of logic , such as Analytical philosophy , for example , have been confronted with vague
phenomena since the universality controversy. The logical positivism tried so-called. Unambiguous ( bijective ) terms to formulate what he though more than in parts of the language has succeeded: even in technical languages unable to make bijectivity, and particularly that is everyday language of uncertainty involved.

Blurring is related to the concept of ambiguity ; however, the concept of fuzziness refers to the object itself that can be represented or imaged, while ambiguity deals with the interpretation of the object. Since the phenomena of blurring and ambiguity are related, blurring can be reduced using similar methods:

• Definitions : Certain linguistic signs can be defined by relating them to an object (→  reference (linguistics) ). However, with vague terms it is difficult to achieve clarity in this way .
• Reference to a core meaning : In prototype semantics , particularly undisputed terms are taken as a starting point in order to then define the other comparable terms within a word field . In this way, greater clarity is achieved, especially with open word fields.
• Contextualization by condensing the language(see also density description ), d. i.e., relates the points of one description to the points of other descriptions.

psychology

Social situations can also be described as fuzzy if the information content is vague and which leaves an observer with a feeling of indefiniteness, indefiniteness or helplessness, so that no clear or satisfactory behavioral variants can be selected as a reaction. This type of situation is interpreted as very uncomfortable, as orientation is perceived as difficult or even impossible. In the worst case, a large number of such situations (experiences) can make you sick.

See scheme (psychology) , pluralistic ignorance (when a person is in an ambiguous, difficult to assess situation and does not know what to do, he looks around to see what the others are doing)

Political science

Sovereign blurring is a term coined by the German political scientist Karl-Rudolf Korte , which, according to Korte, denotes the departure from a pointed political debate. Flexibility in terms of content and the presidential style are increasingly perceived as signs of professionalism. Angela Merkel's political style in particular is often cited by Korte as an example of sovereign blurring.

Individual evidence

1. Ulrich Karrenberg: Signals - Processes - Systems: A multimedia and interactive introduction to signal processing . Springer-Verlag, 2016, ISBN 978-3-662-52659-0 , pp. 65 ff . ( reading sample [PDF]).
2. see Thorsten Roelcke: Technical languages. Berlin 1999, pp. 66-69