DE102008008707A1 - Digital image processing method, involves forming mixed model description depending upon verification, and calculating image values of processed images by considering imaging function from result of mixed model description - Google Patents

Abstract

The method involves generating processed images using an imaging function from raw images. A model is verified in partial regions for image elements (41-49) of the raw images to check whether the model describes local dependence of image values according to given good-criterion. A mixed model description is formed depending upon the verification, where the local dependence of the image values in different image elements is described by different mathematical models. Image values of the processed images are calculated by considering the function from a result of the mixed model description.

Description

The The invention relates to a method for processing digital images, using a mapping function from a digital Raw picture a picture (in the following: "the edited picture") is produced and taking picture values of picture elements of the edited picture under consideration of the mapping function. The invention relates especially the processing of remote sensing image data and here, In particular, more specifically, the sub-field of equalization of the recorded Images.

at the editing of digital images in which the original Image grid is not preserved, such. B. in the equalization of Pictures are known perform a so-called resampling, whereby the intensities (z. Gray values and / or color values) of the picture elements (pixels) in the Raster of the edited image are calculated. The intensities will be also referred to as image values. Under the image grid is the arrangement understood the picture elements in the picture.

Usually will be first from the relationship between the raster of the edited image and the Raster of the raw image determines the imaging function. In the result then lies in the coordinate system of the raw image according to the Imaging function distorted raster of edited image, d. H. the picture elements of the edited image have z. b. diverging (not parallel to each other and usually not rectilinear Borderlines). By the equalization of the raw picture, in which the Pixels in orthogonal rectilinear Rows and columns are arranged, z. B. (as well as a embodiment the invention) the locations of the vertices of the picture elements of the raw image to such divergent, not necessarily straightforward Lines shown. In a picture grid of the new, rectified image, but then z. B. again defined pixels in orthogonal arranged to each other extending rectilinear rows and columns are. As mentioned It is therefore typical for the image editing places the grid of the edited image in Image grid of the raw image by means of a defined mapping function to calculate and the intensities the pixels of the edited image accordingly. This is called resampling.

ever lower the geometric resolution the raw picture is the more common contains a picture element of the raw image shares of different real (by the picture shown) objects, which are thus no longer separated in the picture can be. This case is common in images obtained by remote sensing (eg, by cameras or scanners in satellites or aircraft). The invention relates in particular to the processing of images from such a remote sensing, but may also be useful for other tasks be applied, which images, the relatively many mixing elements (Picture elements with shares from different objects) to be brought into a different geometry.

Because of ignorance of the true distribution of intensity within the individual picture elements arise during the resampling error. Purpose of Invention is to improve the accuracy of the resampling and to make the picture more realistic.

• 1. Das einfachste Verfahren ist das Nearest-Neighbour-Verfahren, bei dem der Bildwert (z. B. Grauwert) desjenigen Bildelementes verwendet wird, welches der berechneten Position am nächsten liegt. Dieses Verfahren produziert zwar optisch scharfe Bilder, erzeugt jedoch speziell an kontrastreichen Bildstrukturen wie z. B. Objektkanten sehr große Fehler.
• 2. Etwas geringere Fehler erhält man bei der bilinearen Interpolation. Bei diesem Verfahren gehen je nach Lage der berechneten Position die Bildwerte von ein bis vier Bildelementen in die Berechnung des Resamplingwertes ein. Die Wichtung erfolgt nach dem Abstand zwischen der errechneten Position und dem betreffenden Bildelement. Dieses Verfahren erzeugt durch die Verschleifung von scharfen Strukturen unscharfe Bilder.
• 3. Eine weitere Gruppe von Verfahren benutzt zentralsymmetrische Wichtungsfunktionen, bei denen das größte Gewicht an der berechneten Position liegt und die gleich einer gedämpften Schwingung mit zunehmendem Abstand abklingen. Ausgangspunkt für diese Art von Wichtungsfunktionen ist die sinx/x-Funktion. Diese Verfahren, zu denen z. B. die kubische Faltung gehört, erzeugen schärfere Bilder als die bilineare Interpolation und rufen kleinere Fehler als das Nearest-Neighbour-Verfahren hervor. Ein wesentlicher Nachteil ist aber, dass bei bestimmten Bildstrukturen durch die negativen Anteile der Wichtungsfunktionen negative Resamplingwerte entstehen können.
• 4. Aus diesem Grunde wurde noch eine andere Gruppe von Verfahren entwickelt, die ebenfalls zentralsymmetrische Wichtungsfunktionen verwendet. Diese Funktionen verlaufen aber nur im positiven Bereich. Sie haben ihr Maximum ebenfalls an der berechneten Position und fallen von dort aus mit wachsendem Abstand ab. Die Eigenschaften dieser Gruppe liegen zwischen der bilinearen Interpolation und den Wichtungsfunktionen der dritten Gruppe (sinx/x-Prinzip).

Known resampling methods can be divided into four types.

• 1. The simplest method is the Nearest Neighbor method, which uses the image value (eg, gray value) of the pixel closest to the calculated position. Although this method produces visually sharp images, but produces especially on high-contrast image structures such. B. Object edges very large errors.
• 2. Slightly lower errors are obtained in bilinear interpolation. Depending on the position of the calculated position, the image values of one to four pixels are included in the calculation of the resampling value. The weighting takes place according to the distance between the calculated position and the relevant picture element. This process produces blurred images by blurring sharp structures.
• 3. Another group of methods uses center-symmetric weighting functions in which the largest weight is at the calculated position and which equal to a damped vibration decays with increasing distance. The starting point for this type of weighting function is the sinx / x function. These methods, which z. For example, when cubic convolution is heard, sharper images are produced than bilinear interpolation and cause smaller errors than the nearest neighbor method. A significant disadvantage, however, is that with certain image structures, negative resampling values can arise due to the negative components of the weighting functions.
• 4. For this reason, yet another group of methods has been developed that also uses center-symmetric weighting functions. These functions are only positive. You also have your maximum at the calculated position and fall from there with increasing Ab stood off. The properties of this group lie between the bilinear interpolation and the weighting functions of the third group (sinx / x principle).

• a) Keines dieser Verfahren beachtet die wirkliche Form und Ausdehnung der Fläche, die den Resamplingwert beeinflusst.
• b) Alle genannten Verfahren betrachten die Elemente des Rohbildes, aus denen der Resamplingwert berechnet wird, als homogen (d. h. einen konstanten Bildwert aufweisend), was in der Realität nur selten der Fall ist.
• c) Keines der bekannten Verfahren stellt sicher, dass das Intensitätsintegral über eine beliebige Fläche im Raster des Rohbildes erhalten bleibt.

However, all known resampling methods have the following disadvantages in addition to the process-specific deficiencies already mentioned:

• a) None of these methods takes into account the actual shape and extent of the area that affects the resampling value.
• b) All these methods consider the elements of the raw image from which the resampling value is calculated to be homogeneous (ie having a constant image value), which is rarely the case in reality.
• c) None of the known methods ensures that the intensity integral is maintained over any area in the raster of the raw image.

All general and procedural deficiencies lead previously known methods to intensity errors in the resampled picture.

aim The invention is to avoid or mitigate the mentioned defects both the middle (above the image or a portion of the image averaged) as well the maximum (occurring at any location of the image) Reduce resampling errors.

Basic considerations underlying the invention are as follows:
In order to achieve a flawless resampling, the raw image would have to be finely resolved since the resampling value (ie the image value of the processed image) is calculated by integrating the image values of the raw image over the area of the new pixel given by the mapping function.

One another case where a flawless resampling value is created, exists when the image value in the captured by the pixel scene completely is homogeneous. In complete homogeneity All resampling methods are equivalent. Both cases are coming in relation to a whole picture in reality not present.

Around to improve the resampling anyway, it is a basic idea of present invention, the resolution of the raw image through models to improve, d. H. to refine.

Preferred dimensions are intended the models in principle to be able to any arbitrary fine Resolution too achieve. Actually achieved resolution may depend in particular on the raw image. But that does not mean that the intensity course within the picture elements with this fine resolution exactly is reproduced, but only approximately. Especially For example, the resolution achieved by the model may vary across the image area.

According to the invention At least two different models are used. Preferably Two models are used. However, there may be more than two Models are used. The number of models is not limited. In practice, however, one will for reasons of limiting the computational effort limit the number of models. Preferably, at least one of Models used that are still described in the figure description become.

The Properties of the models used should be as possible clearly distinguish. For example, you can in the models mathematical functions are used within of a picture element assume one or more extreme values. The functions descriptive z. B. the image value depending on the location in the image.

• – unter Verwendung einer Abbildungsfunktion aus einem digitalen Rohbild ein bearbeitetes Bild erzeugt wird. Insbesondere kann ein orthogonales (z. B. quadratisches) Raster des bearbeiteten Bildes gewählt werden, sodass die Abbildungsfunktion die geometrische Beziehung zwischen dem Raster des Rohbilds und dem Raster des bearbeiteten Bildes definiert.
• – Bildwerte von Bildelementen des bearbeiteten Bildes unter Berücksichtigung der Abbildungsfunktion berechnet werden (dies wird als Resampling bezeichnet).

In particular, a method for editing digital images is proposed, wherein

• A processed image is generated using a mapping function from a raw digital image. In particular, an orthogonal (eg, square) raster of the processed image may be chosen such that the mapping function defines the geometric relationship between the raster of the raw image and the raster of the processed image.
• - Image values of pixels of the processed image are calculated taking into account the mapping function (this is called resampling).

• a) Das Rohbild wird durch zumindest zwei verschiedene mathematische Modelle beschrieben, wobei jedes Modell ausgestaltet ist, Bildwerte eines Rohbildes ohne vorgegebene örtliche Rasterung in Abhängigkeit des Bildortes zu beschreiben, sodass das Rohbild durch das jeweilige Modell mit feinerer örtlicher Auflösung beschreibbar ist.
• b) Zumindest in Teilbereichen des Rohbildes wird für jedes Bildelement geprüft, welches Modell die örtliche Abhängigkeit der Bildwerte innerhalb des Bildelementes (wahrscheinlich) besser wiedergibt, und/oder es wird zumindest in den Teilbereichen für jedes Bildelement ein Modell daraufhin geprüft, ob es die örtliche Abhängigkeit der Bildwerte entsprechend einem vorgegebenen Güte-Kriterium beschreibt. Vorzugsweise wird jedes Bildelement des Rohbildes derart geprüft.
• c) Abhängig von der Prüfung wird gegebenenfalls eine gemischte Modellbeschreibung gebildet, in der die örtliche Abhängigkeit der Bildwerte in verschiedenen Bildelementen des Rohbildes durch verschiedene mathematische Modelle (d. h. in jedem Bildelement durch eines der zumindest zwei verschiedenen mathematische Modelle) beschrieben wird.
• d) Bildwerte des bearbeiteten Bildes werden unter Berücksichtigung der Abbildungsfunktion aus dem Resultat der gemischten Modellbeschreibung (insbesondere durch Integration über eine Teil-Fläche des Rohbildes wie es durch die gemischte Modellbeschreibung beschrieben wird) berechnet.

Resampling contains the following:

• a) The raw image is described by at least two different mathematical models, each model being designed, image values of a raw image without predetermined local screening depending on of the image location so that the raw image can be described by the respective model with a finer spatial resolution.
• b) At least in partial areas of the raw image, it is checked for each pixel which model (probably) better reflects the local dependence of the image values within the pixel and / or at least in the partial areas for each pixel a model is checked to see if it is the local Dependence of image values according to a given quality criterion describes. Preferably, each pixel of the raw image is checked in such a way.
• c) Depending on the test, a mixed model description is formed if necessary, in which the spatial dependence of the image values in different pixels of the raw image is described by different mathematical models (ie in each pixel by one of the at least two different mathematical models).
• d) Image values of the processed image are calculated taking into account the mapping function from the result of the mixed model description (in particular by integration over a partial area of the raw image as described by the mixed model description).

• – Es werden Parameter einer Modellfunktion bestimmt, die den örtlichen Verlauf der Bildwerte des Rohbildes, wie er durch ein bestimmtes Modell in einer Nachbarschaft des Bildelementes beschrieben wird, lediglich begrenzt auf die Nachbarschaft wiedergibt. Anders ausgedrückt wird die Modellfunktion im Bereich der Nachbarschaft in das Modell gefittet. Dabei kann es sich bei der Modellfunktion um eine Funktion handeln, die bereits in mindest einem der Modelle verwendet wurde, z. B. als Zwischenschritt bei der Berechnung der Bildwerte mit feinerer örtlicher Auflösung. Die Nachbarschaft des Bildelementes wird durch zumindest einen Teilbereich des zu prüfenden Bildelements selbst und durch einen weiteren, dem zu prüfenden Bildelement benachbarten Bereich gebildet. Der weitere Bereich liegt lediglich auf einer Seite des zu prüfenden Bildelementes. Beispielsweise wird der weitere Bereich durch die Fläche der (zwei oder mehr; die Mindestanzahl ist durch die verwendete Funktion definiert) Bildelemente des Rohbildes definiert, die sich auf der Seite ausgehend von dem Rand des zu prüfenden Bildelementes hintereinander in geradliniger Richtung erstrecken, z. B. in Zeilenrichtung oder Spaltenrichtung, je nachdem um welche Seite es sich handelt. Z. B. kann ein Bildelement in einem orthogonalen Raster mit Bildelementen, die in Zeilen und Spalten angeordnet sind, vier Seiten haben, jeweils zwei Seiten einander gegenüberliegend in Spaltenrichtung und zwei Seiten einander gegenüberliegend in Zeilenrichtung. Z. B. zwei dieser Seiten (d. h. eine Seite in Zeilenrichtung und eine Seite in Spaltenrichtung können jedoch alternativ auch als eine Seite aufgefasst werden, sodass das Bildelement lediglich zwei Seiten hat. Als Ergebnis der Nachbarschaft wird ein erster Parametersatz der Modellfunktion erhalten, d. h. eine erste parametrisierte Modellfunktion.
• – Der zuvor genannte Schritt wird auch für zumindest eine weitere Nachbarschaft durchgeführt, wobei der weitere Bereich dieser Nachbarschaft auf einer anderen Seite des zu prüfenden Bildelementes liegt, sodass für jede weitere Nachbarschaft ein weiterer Parametersatz erhalten wird, d. h. je eine weitere parametrisierte Modellfunktion.
• – Für zumindest einen Ort innerhalb des zu prüfenden Bildelementes oder am Rand des zu prüfenden Bildelementes werden die Bildwerte berechnet, die sich mit der Modellfunktion aus den verschiedenen Parametersätzen ergeben, d. h. aus den parametrisierten Modellfunktionen.
• – Die vorangegangenen Schritte werden für die verschiedenen Modelle ausgeführt. Es wird verglichen, welches Modell an einem oder mehreren Orten des zu prüfenden Bildelementes zu der geringsten Streuung in den aus den Parametersätzen der verschiedenen Nachbarschaften berechneten Bildwerten führt und es wird entschieden, dass das Modell mit der geringsten Streuung das Bildelement in der gemischten Modellbeschreibung beschreiben soll. Im einfachsten Fall, wenn lediglich zwei Parametersätze vorhanden sind, ist die Streuung die Differenz der Bildwerte.
• – Alternativ zu dem vorhergehend genannten Schritt, werden die davor genannten Schritte für ein Modell (separat von dem oder den anderen Modellen oder ausschließlich nur für ein Modell) ausgeführt. Es wird geprüft, ob Abweichungen an einem oder mehreren Orten des zu prüfenden Bildelementes, die sich für die verschiedenen Nachbarschaften ergeben, das vorgegebene Güte-Kriterium erfüllen, und es wird bei Nichterfüllung des Güte-Kriteriums entschieden, dass das zu prüfende Pixel in der gemischten Modellbeschreibung durch ein anderes Modell zu beschreiben ist.

In particular, if no reference image is available for the test in step b), the following steps are preferably carried out for at least one image element of the raw image to be tested:

• - Parameters of a model function are determined, which reflects the local course of the image values of the raw image, as described by a specific model in a neighborhood of the pixel, only limited to the neighborhood. In other words, the model function is fitted in the vicinity of the model. The model function may be a function that has already been used in at least one of the models, e.g. B. as an intermediate step in the calculation of image values with finer local resolution. The neighborhood of the picture element is formed by at least a partial area of the picture element to be tested itself and by another area adjacent to the picture element to be tested. The further area lies only on one side of the picture element to be tested. For example, the further area is defined by the area of (two or more, the minimum number is defined by the function used) picture elements of the raw image which extend in a straight line on the side starting from the edge of the picture element under test, e.g. In the row direction or column direction, depending on which side it is. For example, a pixel in an orthogonal raster having picture elements arranged in rows and columns may have four sides, two sides opposite one another in the column direction and two sides opposite to each other in the row direction. For example, two of these pages (ie one page in the row direction and one page in the column direction may alternatively be construed as one page so that the picture element has only two pages.) As a result of the neighborhood, a first parameter set of the model function is obtained, ie a first parameterized model function ,
• The aforementioned step is also carried out for at least one further neighborhood, wherein the further area of this neighborhood lies on another side of the picture element to be checked, so that for each further neighborhood a further parameter set is obtained, ie one more parameterized model function.
• For at least one location within the picture element to be checked or at the edge of the picture element to be checked, the picture values which result from the model parameter function from the various parameter sets, ie from the parameterized model functions, are calculated.
• - The previous steps are performed for the different models. It is compared which model at one or more locations of the pixel under test leads to the least scatter in the image values calculated from the parameter sets of the different neighborhoods and it is decided that the model with the lowest dispersion is to describe the pixel in the mixed model description , In the simplest case, if there are only two parameter sets, the scatter is the difference of the image values.
• - As an alternative to the previous step, the above steps are performed for a model (separate from the other model (s), or only for one model). It is checked whether deviations at one or more locations of the pixel under test, which result for the different neighborhoods, meet the predetermined quality criterion, and it is decided in case of failure of the goodness criterion that the pixel under test in the mixed Model description is to be described by another model.

general formulated can, if no reference image is present, the local History of the image values provided by the model at different Pages of the to be tested Picture element are examined. This is to be understood by course, that the direction of the course is transverse (eg perpendicular) to a boundary of the test to be tested Picture element is. The course also has to be the picture element to be checked to capture.

• – Für zumindest einen Teilbereich des Rohbildes werden Quotienten der aus dem zu prüfenden Modell oder den zu prüfenden Modellen einerseits und den Bildwerten des Referenzbildes andererseits gebildet, sodass für jedes zu prüfende Modell ein Quotienten-Bild entsteht. Dabei kann durch den Bildwert des Referenzbildes geteilt werden oder durch den Bildwert des Modells.
• – Für das zu prüfende Bildelement wird ein Maß berechnet, das beschreibt, wie ausgeprägt ein gegebenenfalls an einem Ort in dem zu prüfenden Bildelement vorhandenes lokales Extremum der Bildwerte des Quotienten-Bildes im Vergleich zu der Umgebung des Bildelementes ist. Das Maß ist z. B. die größte Differenz des Extremwertes zu einem der acht Umgebungswerte (d. h. Werte der acht unmittelbar benachbarten Bildelemente) in einer 3 × 3 Nachbarschaft. Alternativ wird für ein zu prüfendes Bildelement und seine Umgebung ermittelt, ob der Bildwert des Quotienten-Bildes innerhalb der Umgebung ein Extremwert bezüglich einer geringeren Anzahl von Umgebungswerten, z. B. mindestens zwei gegenüberliegenden Umgebungswerten ist.
• – Die vorangegangenen Schritte werden für die verschiedenen Modelle ausgeführt. Es wird ermittelt, welches Modell an einem oder mehreren Orten des zu prüfenden Bildelementes ein lokales Extremum aufweist und gegebenenfalls in welchem Modell der Extremwert am geringsten ausgeprägt (z. B. das Maß den geringsten Wert liefert) ist. Es wird entschieden, dass das Modell mit der geringsten Ausprägung des lokalen Extremums bzw. ein Modell ohne Extremwert das Bildelement in der gemischten Modellbeschreibung beschreiben soll.
• – Alternativ zu dem vorhergehend genannten Schritt, werden die davor genannten Schritte für ein Modell (separat von dem oder den anderen Modellen oder ausschließlich nur für ein Modell) ausgeführt. Es wird geprüft, ob das Modell an einem oder mehreren Orten des zu prüfenden Bildelementes ein lokales Extremum aufweist. Es wird bei Vorhandensein des Extremums entschieden, dass das zu prüfende Pixel in der gemischten Modellbeschreibung durch ein anderes Modell zu beschreiben ist, oder dann durch ein anderes Modell zu beschreiben ist, wenn die Ausprägung des Extremums in dem anderen Modell geringer ist.

In particular, if a reference image is available for the test in step b), the following steps are performed during the test for at least one image element of the raw image to be tested:

• For at least a subarea of the raw image, quotients of the models to be tested or the models to be tested on the one hand and the image values of the reference image on the other hand are formed so that a quotient image is produced for each model to be tested. It can be divided by the image value of the reference image or by the image value of the model.
• For the picture element to be checked, a measure is calculated which describes how pronounced a local extremum of the image values of the quotient image, if appropriate at a location in the picture element to be tested, is in comparison to the surroundings of the picture element. The measure is z. For example, the maximum difference of the extreme value to one of the eight environmental values (ie, values of the eight immediately adjacent pixels) in a 3 × 3 neighborhood. Alternatively, for a pixel under test and its environment, it is determined whether the image value of the quotient image within the environment is an extreme value with respect to a lower number of environmental values, e.g. B. is at least two opposite environmental values.
• - The previous steps are performed for the different models. It is determined which model has a local extremum at one or more locations of the pixel under test and, if appropriate, in which model the extreme value is the least pronounced (eg the measure gives the lowest value). It is decided that the model with the lowest expression of the local extremum or a model without extreme value should describe the picture element in the mixed model description.
• - As an alternative to the previous step, the above steps are performed for a model (separate from the other model (s), or only for one model). It is checked whether the model has a local extremum at one or more locations of the pixel under test. It is decided in the presence of the extremum that the pixel to be tested in the mixed model description is to be described by another model, or to be described by another model when the expression of the extremum in the other model is lower.

The inventive method is z. B. on a commercial Computer or computer network. The scope of the invention belongs Therefore, a device for carrying out the method, for. B. a computer or a computer network, wherein the device means (eg, software) that are configured, the method in one of its embodiments.

embodiments The invention will now be described with reference to the accompanying drawings described. The individual figures of the drawing show:

1 a subarea of a raw image with a total of nine quadratic pixels,

2 four of the picture elements according to 1 with triangular subdivisions to represent a first mathematical model to refine the local resolution,

3 the four pixels according to 2 and a pixel of a processed image whose rasterization does not match the rasterization of the raw image,

4 a first example to explain the operation of a second mathematical model,

5 a second example to illustrate the operation of the second mathematical model,

6 a picture element of the raw image which has been resolved locally finer by the second mathematical model, wherein the picture element contains three homogeneous regions,

7 another pixel of the raw image resolved locally refined by the second mathematical model, the pixel containing four homogeneous regions,

8th four image elements of the raw image in a mixed model description and four image elements of the processed image for the representation of the process step, in which the image values of the image elements of the processed image are calculated by integration over partial regions in the raw image.

9 a representation similar to the one in 1 to explain the second mathematical model.

1 shows nine picture elements of the raw picture in an orthogonal picture grid, ie three pictures each elements per line or per column of the image grid. The pixel in the middle of this 3 × 3 environment 41 is strongly edged to highlight it. The other elements of the 3 × 3 environment are denoted by the reference numerals 42 to 49 designated. The picture element 41 already has a subdivision in the form of triangular areas, which will be discussed below in the description of the first mathematical model. This first model is called a continuous model.

At the continuous model is going through a local area of the raw image described a mathematical function. The type of function determines doing the size of the local Range. If z. A quadratic function (i.e., a polynomial second degree), so you need three support values, So three picture elements. In other embodiments of the continuous Model can however, other mathematical functions are used. this applies also for the model functions described below for determining the best mathematical model.

W₁, W₂, W₃ sind dabei die Bildwerte des ersten, zweiten und dritten Bildelementes (z. B. W₁ der Bildwert von Pixel 43, W₂ der Bildwert von Pixel 41 und W₃ der Bildwert von Pixel 48). a, b, c sind die Parameter der quadratischen Funktion. x ist die Ortsvariable, wobei es sich um eine reelle Zahl handelt. Die zugehörige x-Achse verläuft im Beispiel der Pixel 43, 41, 48 in Spaltenrichtung durch die Pixel hindurch.The continuous model will now be explained using a quadratic function as an example. So it is to find a quadratic function whose integration over the width or length of each pixel exactly gives the associated image value. The image values of three consecutive picture elements (eg the sequence of the picture elements 43 . 41 . 48 in 1 ) in the direction of an image axis (the image axis runs in 1 in the column direction or in the row direction) result in this model by integration over in each case a parabolic piece, ie:

W ₁ , W ₂ , W ₃ are the image values of the first, second and third image elements (eg W _{1 is} the image value of pixels 43 , W _{2 is} the image value of pixels 41 and W _{3 is} the image value of pixels 48 ). a, b, c are the parameters of the quadratic function. x is the location variable, which is a real number. The associated x-axis runs in the example of the pixels 43 . 41 . 48 in the column direction through the pixels.

durch Auflösung des Gleichungssystems, das aus diesen drei Gleichungen besteht, können die Koeffizienten (d. h. die Parameter) der quadratischen Funktion berechnet werden.By calculating the three integrals one obtains:

By solving the system of equations consisting of these three equations, the coefficients (ie, the parameters) of the quadratic function can be calculated.

In the same way, a further quadratic function is now formed from the picture elements (for example pixels 41 . 48 and a column direction immediately below pixels 48 located pixel). W ₄ denotes the image value in the raw image of below pixel 48 located pixels. As a rule, other coefficients will result, ie the respective function applies only to the three picture elements from which it was calculated.

In order to ensure the necessary continuous transition between the now two quadratic functions present, a distance-dependent weighting is introduced. The single weight results z. B. in linear declining weighting G = 1 - E with G = weight and E = distance from the center. Should z. For example, if the resulting function value RW is calculated at the midpoint point of W1 + 0.3, the result is linear weighting RW = 0.7 · LW 1 + 0.3 · LW 2 where LW ₁ and LW _{2 are} the local function values of the first and second quadratic functions at the point to be calculated, respectively. The named place is in 1 marked by a cross, with the reference numeral 51 is designated.

It can but also other distance-dependent Weights are used. This way can be a continuous Image values function (also called "intensity function" in the following) in the direction of an image axis be prepared and also by the same procedure in the direction the second image axis (which is usually perpendicular to the first image axis runs) a continuous two-dimensional intensity function over the whole image.

These two-dimensional continuous function is no longer analytic writable and therefore not closed integrated (The integration is used in the calculation of the image values of the edited Picture performed, even closer will be described). This means that the two-dimensional function of the Picture must be converted into an integrable function, because the value of one over the original Raster offset pixel is calculated by integration.

Therefore, in the embodiment of the continuous model described here, the continuous two-dimensional intensity function is represented by triangular areas (see division of the area of the pixel 41 in 1 in z. B. a total of eight triangular areas) approximated. Intensities (image values) are defined at the interpolation points (the corner points) of the individual triangles. Since the support points are at the same time the support points of adjacent triangles, the triangles in the three-dimensional space are connected to each other continuously (without discontinuities). The intensity within the triangular faces is a function of the location in the xy plane of the triangle, where the x, y coordinates are a Cartesian coordinate system. In this way you get at each point of the triangle area receives a certain intensity. In principle, therefore, each location in the xy plane can have a different intensity, ie the model is in principle infinitely finely resolving.

As the intensity by inserting the location coordinates (x, y) into the respective one Triangle-related level equation can be calculated is described below. Also the calculation the parameter of the plane equation from the intensities at the reference points will be explained below.

Because of this description by triangular surfaces, the continuous intensity function only has to be calculated at certain support points, namely at the vertices of the triangles. The accuracy of the fitting depends on the number of triangles per pixel. As the number increases, however, the calculation effort also increases. A preferred division is the one mentioned in pixels 41 in 1 ,

Because of the interpolation between the individual functions over mutually offset image areas (see above) and the described approximation of the continuous function by triangular surfaces, the requirement for the constancy of the intensity integral (in the calculation of the image elements of the processed image) is no longer met. However, the constancy can preferably be restored by the following correction:
In 2 are four adjacent picture elements 41 . 46 . 48 . 49 shown in the same way as in 1 at pixel 41 divided into eight triangles each. Now, if the intensity at the support point P1 changed so be this influences all four picture elements via the eight triangular edges emanating from this support point. So z. For example, increasing the intensity at the interpolation point P1 will increase the intensity of all eight triangles associated with that interpolation point at this point and thus increase the integral intensity among the triangular areas (ie the intensity obtained by integration over the triangular areas). If the intensity at the interpolation point P2 is changed, only two picture elements are affected (namely pixels 41 and 46 ) and the change at the support point P3 only one picture element (pixel 49 ).

Since the change of the intensity integral of a triangle is defined when a supporting value is changed, the necessary change in the reference value can be calculated directly. This is illustrated by the following example:
Any level can use the function z = m * x + n * y + c to be discribed. Where z is the function value at the point (ie location) (x, y) and m, n, c are parameters of the function.

c = z1 – m·x1 – n·y1 Each plane is defined by three points P (x, y, z). If the points are inserted in the plane equation, then one obtains according to parameters resolved:

c = z 1 - mx 1 - n · y 1

All triangles of the continuous model are rectangular and, if the right angle were in the origin, would have the coordinates x 1 = 0; y 1 = 0; x 2 = 1 2 ; y 2 = 0; x 3 = 0; y 3 = 1 2 ;

This simplifies n, m, and c to: n = 2 · (z 3 - z 2 ) m = 2 · (z 2 - z 1 ) c = z 1

The intensity I of an arbitrarily inclined triangle (arbitrary value of the support points) is:

und nach Einsetzen der Integrationsgrenzen I = m48 + n48 + c8 After y and x integrated you get

and after inserting the integration limits I = m 48 + n 48 + c 8th

at a change from z3 or z2 (support points at the acute angles of the triangle) you get the double change from n or m, d. H. at change of z3 or z2 changes by the value 1 the value of the integral is 1/24. When changing z1 (interpolation point at the right angle of the triangle) by 1, the value of the integral changes at 1/8. Thus, for a desired change of the integral value directly the necessary change of the reference value be specified.

First become the support values changed, affect the four picture elements. These corrections, which simultaneously change four picture elements, are made when the differences between the integrals all four picture elements and the intensities of the corresponding picture elements have the same sign. The smallest difference determines the size of the correction, because in each case only the error portion is to be corrected, which in is included in all four picture elements. If the correction of this Kind of support values about that whole picture was taken, next are the supporting values changed, the two picture elements influence, again the signs the differences must be equal and the smallest difference is. The remaining bugs now only affect individual ones Picture elements and are by change the center points corrected. Thereafter, the intensity constancy is restored throughout the image.

For each triangle within a picture element, as explained above, the plane equation defined by the 3 interpolation points (intensities at the corner points of the triangles) is set up. The resampling value (ie, the image value of the pixel to be calculated 53 , please refer 3 , the processed image) now results from the sum of the integrals over all triangular faces or triangular sub-faces which lie in the area of the raw image which results from the projection of the corresponding quadratic picture element of the processed image with the aid of the imaging function. For triangles that are completely within the current raw image area, the integration boundaries are the triangle sides, while for incomplete triangles, the boundary of the projected image element of the processed image may also be an integration boundary. Both cases follow the example 3 in front. z. B. is the triangle 54 completely contained in the area over which it is integrated. Other triangular areas are partly located both inside and outside the area.

Now a second model is described that z. B. in addition to the continuous model and / or in addition to another model for the Refinement of the local resolution of the raw image is used. This model is also called homogeneous Model designates.

The homogeneous model assumes that the mapped area homogeneous surfaces exists, d. H. the image value is constant within a homogeneous area. The image value in a homogeneous area can, in particular dependent on the size of the area, a Extreme value (maximum or minimum) of the image value or he can an average of a larger subarea of the Be raw picture. In the latter case, the homogeneous surface is about equal to the area the picture elements of the raw image whose average value the image value is. As the pixel boundary in the raw image is usually not coincides with the boundary of a homogeneous surface, arise in homogeneous model picture elements (ie the homogeneous surfaces), the may be referred to as mixing elements.

Now becomes a preferred embodiment of the homogeneous model: Does not lie in a homogeneous area exact homogeneity before (i.e., the image values of the picture elements of the raw image, which are represented by the homogeneous surface summarized, not exactly the same), it is decided whether a picture element is to belong entirely to a homogeneous surface, or whether as a mixing element is defined. This decision will be made on the following one-dimensional Examples explained.

Example 1 is in 4 shown. In the top line of 4 the image values I are plotted for an order of seven pixels of the raw image. For example, there are successive picture elements in a line or a column of an orthogonal image grid of the raw image. In the bottom line of 4 the differences D of the image values are plotted for every two directly adjacent picture elements of the raw image, which result from the image values in the upper line.

A local minimum in the differences indicates a homogeneous area, ie the picture elements with the image values 50 and 48, as well as 41 and 39 are defined in the model as homogeneous areas. Since the image value 45 of the pixel lying between these two homogeneous areas is not an extreme value, this pixel is defined as a mixing element. Ie. this picture element is shared and it becomes the newly created one Homogeneous surfaces each assigned an image value corresponding to the value of belonging to the homogeneous surface adjacent pixel. For example, would in 4 the mixing element with the value 45 can be divided into two parts with the values 48 (left neighbor element) and 41 (right neighbor element).

general formulated the mixing element or from the original Pixel formed new picture elements (these are in the two-dimensional Case under circumstances more than two pixels) satisfy the condition that the area weighted Average value of the new picture elements equal to the picture value of the original Picture element is.

Example two is in 5 shown. In the top line are like in 4 the adjacent image values are plotted in one direction. In turn, the differences between the image values of immediately successive, ie adjoining, pixels are plotted on the lower line. In this example, the two homogeneous areas (which originated from the original picture elements with the picture values 50 and 48 or from the picture elements with the picture values 45 and 43) immediately adjoin one another. There is no mixing element between these newly formed homogeneous surfaces according to the model.

The two examples according to 4 and 5 have explained the basic principles of the embodiment of the homogeneous model. It is possible to summarize the exact criteria of the model for the formation of homogeneous surfaces (eg how many neighboring pixels are combined to a homogeneous surface in which differences in the image values or which differences between the image values of adjacent pixels compared to differences of others Neighbors are interpreted as an indication of an extreme value). As a result, a finer or less fine local resolution can be achieved. The model may alternatively or in addition to the differences of the image values of adjacent pixels use other calculation methods, eg. B local derivatives of functions fit into image values of pixels in rows or columns.

It will now describe how the homogeneous model in the case of a real, two-dimensional raw image is formed. In two-dimensional Case can be a difference in image values between two, three or even four contiguous homogeneous surfaces occur, d. H. it can Boundary lines between two homogeneous surfaces and boundary points with three or four adjacent homogeneous surfaces.

If the transition occurs only in one direction (eg, in the row direction or column direction), as is the case at a boundary line between two homogeneous surfaces, the location x of the boundary line in a mixing element between the homogeneous regions is calculated as follows: x · WN 1 + (1 - x) · WN 2 = WM

there WM is the image value of the mixing element. WN1 is the left or upper neighbor element and WN2 the right or lower neighbor element.

In this way, in the exemplary embodiment, the boundary lines for all transitions between two homogeneous surfaces are first calculated, each having two end points on the border of the picture element, such. B. the picture element 3 in 8th , These endpoints are starting points for the division of the mixing elements, which consist of three (see example in FIG 6 ) or four (see example in 7 ) consist of homogeneous surfaces.

In 6 denotes the reference numeral 61 the square edge of a mixing element, ie the edge of a surface which corresponds to the surface of a picture element of the original raw image. There are three homogeneous surfaces in it 62a . 62b . 62c recognizable, thus having a common boundary point, denoted by the reference numerals 63 is designated.

In 7 denotes the reference numeral 71 the square edge of a mixing element, ie the edge of a surface which corresponds to the surface of a picture element of the original raw image. There are four homogeneous surfaces in it 72a . 72b . 72c . 72d recognizable, thus having a common boundary point, denoted by the reference numerals 73 is designated.

First, the merge element is divided by lines from the midpoint M of the face to the endpoints. 9 shows this case for a mixing element similar to the mixing element 61 according to 6 , The endpoints are denoted by the reference numerals 65a . 65b and 65c designated. The lines to the center M are in 9 drawn as continuous lines.

By weighting the image values of the resulting homogeneous areas within the blending element in accordance with their area proportions and thus calculating the average image value, one usually obtains an average value that does not match the image value of the original picture element. By shifting the midpoint M in the direction of the largest difference of the image values of the neighboring elements, in a preferred embodiment the average image value is adjusted to match the image value of the original pixel. Is z. For example, the difference between the image values of the upper and lower neighbor elements of Element 61 in 9 greater than the difference in image values between the left and right neighbor elements, the center becomes a point in the vertical direction 63 shifted until the average image value from the individual sub-areas is equal to the image value of the original picture element. This also changes the course of the boundary lines between the homogeneous surfaces. 9 indicates by an arrow the assumed direction of displacement for the midpoint. The new boundary lines achieved by the shift are shown as broken lines.

In other words, shifting the center point to the point 63 according to 6 shifted and the course of the boundary lines between the homogeneous surfaces shown there 62 set.

Now gets out of the models (eg for the homogeneous model and the continuous model, or for another Combination of models) for every picture element of the original one Raw image each selected the one that the local dependence the image values within the picture element probably better (or in more than two models, best). Preferred embodiments are described below.

In a first case is additional to the raw image no further information available, d. H. it is in particular no reference picture before. For this case is being examined whether different model functions provide evidence that the respective Model the local dependence approximating the image values correctly describes. In particular, the following procedure is proposed: for one A plurality of locations in the raw image are each a plurality of Functions fit, d. H. they become fit parameters of the functions certainly. It is for the fit with a function selected in each case a portion of the image, z. B. a picture element in which the place is located and in addition one Number of picture elements that are in a straight line to the picture element to be located with the place. In particular, the same place will be different Subareas of the image selected and each fitted a function. In this way, the gradients, which result from the fit functions compared at the place become. Distinct differences arising from the functions in the place resulting image values indicate that the respective model the local dependence the image values are not correct and vice versa.

• 1. Bildelement 41, Bildelement 45 und ein weiteres Bildelement links neben Bildelement 45 in derselben Zeile wie Bildelemente 41, 45.
• 2. Bildelement 41, Bildelement 46 und ein weiteres Bildelement rechts neben Bildelement 46 in derselben Zeile wie Bildelemente 41, 46
• 3. Bildelement 41, Bildelement 43 und ein weiteres Bildelement oberhalb von Bildelement 43 in derselben Spalte wie Bildelemente 41, 43
• 4. Bildelement 41, Bildelement 48 und ein weiteres Bildelement unterhalb von Bildelement 48 in derselben Spalte wie Bildelemente 41, 48.

In the embodiment now described, at the nine vertices of the triangular faces of the picture element 41 according to 1 each calculated image values from four functions, which were fit into parts of the raw image. The subareas are as follows:

• 1st picture element 41 , Picture element 45 and another picture element to the left of the picture element 45 in the same line as picture elements 41 . 45 ,
• 2nd picture element 41 , Picture element 46 and another picture element to the right of the picture element 46 in the same line as picture elements 41 . 46
• 3rd picture element 41 , Picture element 43 and another picture element above picture element 43 in the same column as picture elements 41 . 43
• 4th picture element 41 , Picture element 48 and another picture element below picture element 48 in the same column as picture elements 41 . 48 ,

It the scattering of the image values at the nine vertices is calculated in each case.

A possibility the evaluation is the following: Exceeds the scatter (z. B. the mean of the four function values) a predetermined Limit, the homogeneous model is used for this pixel. Otherwise, the continuous model is used.

at the use of multiple models, the model is used where the four possible combinations produce the least scattering at the vertices of the triangular surfaces. The scatter of the individual models can also be weighted.

If a reference image is present, so this is additional Information used to decide which of the two or more Models each for a picture element is used.

In a specific embodiment, a quotient image is calculated in which the value at a specific location of the raw image results from the division of the reference image value by the corresponding result value of the continuous model. The reference image refers to the same grid as the edited image or is defined in the same location coordinate system as the edited image. Extreme values in a 3 × 3 environment ( 1 shows such a 3 × 3 environment, but for the raw image) in the quotient image are considered as an indication of a resampling error. An extremum in a 3x3 environment is understood herein to mean that the image value of the quotient image for the pixel in the center of the environment is a minimum or maximum within the environment.

When Extreme value, a picture element can be defined however also, if it opposite less than eight neighboring pixels, but at least two opposite Neighboring elements represents an extremum. The probability a resampling error decreases with decreasing number of neighboring elements from.

Based on 8th example will be explained. Is z. B. the picture element 5 of the quotient image (here becomes picture element 5 considered an image element of the quotient image) an extreme value, this can be due to an incorrect division of the picture elements 1 to 4 to have emerged from the raw picture. Therefore, the model description and the elements 1 to 4 replaced successively by the homogeneous model. By inserting the homogeneous model, in turn, several elements of the result image (ie the processed image) and thus also the quotient image are influenced. So z. B. the model change in the element 4 an influence on the elements 5 to 8th , If the scattering of the influenced elements in the quotient image decreases as a result of the model change, the model change is confirmed, ie the homogeneous model prevails. Otherwise, the continuous model will persist at this point.

If more than two models are used, then in the example shown, the division of the elements 1 to 4 not only by the homogeneous model but also by the other models and confirming the model for the corresponding element which produces the least scatter in the quotient image for the affected elements

In particular, after it has been decided for each picture element of the raw picture which model best describes the local dependency of the picture values within the picture element, the mixed model description of the raw picture is fixed. In the mixed model description, the local dependence of the image value for each pixel is described by the model that is best for the pixel. 8th shows such a mixed model description for four picture elements 1 . 2 . 3 . 4 which are bounded by wide lines running in horizontal and vertical directions. Within the picture elements 1 . 2 . 4 the triangular representation is recognizable. This indicates that the continuous model is used for these picture elements in the exemplary embodiment described here. In contrast, for the picture element 3 found that the homogeneous model is the best model. Therefore, in the picture element 3 a division into two homogeneous surfaces recognizable.

The The resampling value is now calculated by integration over the respective area the picture elements of the edited image using the information about the Mapping function (that is, the transformation of the grid) that the transition from the raw image to the edited image. In other words, go into the integration for a certain picture element of the edited picture usually subareas of several pixels of the raw image. The image values of this subareas are weighted according to the proportion of the partial area in the total area.

8th also shows four pixels surrounded by dotted lines 5 . 6 . 7 . 8th the edited image. When calculating the picture value of picture element 5 , partial areas of the picture elements go 1 . 2 . 3 . 4 into the integration.

Claims (3)

Method of processing digital images, wherein - using a mapping function from a raw image ( 1 . 2 . 3 . 4 ) a processed image ( 5 . 6 . 7 . 8th ) and - image values of image elements of the processed image ( 5 . 6 . 7 . 8th ) are calculated taking into account the mapping function (resampling), characterized in that in the resampling a) the raw image ( 1 . 2 . 3 . 4 ) is described by at least two different mathematical models, wherein each model is designed to describe image values of a raw image as a function of the image location, so that the raw image can be described by the respective model with a finer spatial resolution, b) at least in subregions of the raw image ( 1 . 2 . 3 . 4 ) for each pixel, which model is likely to better reflect the spatial dependency of the image values within the pixel, and / or at least in the subregions for each pixel a model is checked to see if it is the local dependency of the image values according to a given quality criterion c) depending on the test, if appropriate, a mixed model description is formed, in which the local dependence of the image values in different picture elements of the raw image ( 1 . 2 . 3 . 4 ) is described by various mathematical models, d) image values ( 5 ) of the edited image ( 5 . 6 . 7 . 8th ) are calculated taking into account the mapping function from the result of the mixed model description. Method according to the preceding claim, wherein in the test in step b) according to claim 1 for at least one pixel to be tested ( 3 ) of the raw image, the following steps are carried out: - parameters of a model function are determined which determine the local course of the image values of the raw image ( 1 . 2 . 3 . 4 ), as represented by a particular model in a neighborhood of the picture element ( 3 ), limited to the neighborhood, the neighborhood of the picture element passing through at least a portion of the picture element under test ( 3 ) itself and by another area adjacent to the pixel under test ( 4 ), the further area ( 4 ) only on one side of the pixel under test ( 3 ), so that a first parameter set is obtained, - the aforementioned step is also used for at least one further neighborhood ( 3 . 1 ), the wider area of this neighborhood ( 3 . 1 ) on another side of the picture element to be tested ( 3 ), so that for each further neighborhood a further parameter set is obtained, - for at least one location within or at the edge of the pixel under test ( 3 ) the image values which result from the model function from the different parameter sets are calculated, the preceding steps are carried out for the different models, it is compared which model is located at one or more locations of the picture element to be checked (FIG. 3 ) leads to the smallest deviations in the image values calculated from the parameter sets of the various neighborhoods and it is decided that the model with the smallest deviations 3 ) in the mixed model description, or, alternatively to the previous step, the above-mentioned steps are executed for a model, it is checked whether deviations at one or more locations of the picture element to be checked ( 3 ), which result for the various neighborhoods that meet the specified quality criterion, and it is decided in the case of non-fulfillment of the quality criterion that the pixel under test ( 3 ) in the mixed model description by another model. The method of claim 1, wherein in the test in step b) according to claim 1 for at least one pixel to be tested ( 3 ) of the raw image ( 1 . 2 . 3 . 4 ) the following steps are carried out: - for at least a portion of the raw image ( 1 . 2 . 3 . 4 ) quotients of the models to be tested or the models to be tested on the one hand and the image values of the reference image on the other hand are formed, so that a quotient image is produced for each model to be tested, for the image element to be tested ( 3 ), a measure is calculated which describes how pronounced a local extremum of the image values of the quotient image, if appropriate at a location in the image element to be tested, is compared to the environment ( 1 . 2 . 4 ) of the picture element ( 3 ) and / or for a picture element to be checked ( 3 ) and its environment, it is determined whether the image value of the quotient image within the environment or a part of the environment is an extreme value, the preceding steps are carried out for the different models, it is determined which model in one or more places of examining picture element ( 3 ) has a local extremum and possibly in which model the extreme value is least pronounced, and it is decided that the model with the lowest expression of the local extremum or a model without extreme value the pixel ( 3 ) in the mixed model description, or, alternatively to the previous step, the above-mentioned steps are executed for a model, it is checked whether the model is located at one or more locations of the pixel under test ( 3 ) has a local extremum, and it is decided in the presence of the extremum that the pixel to be tested ( 3 ) in the mixed model description by another model, or to be described by another model if the expression of the extremum is less in the other model.