DE102006056650A1 - Bilateral filtering method for digital image data, involves modifying pixel value and distance weighting functions using edge weighting function that is determined based on edge strength of image pixel - Google Patents

Abstract

The method involves determining a smoothing pixel value for a pixel value of an image pixel of an image data, where the smoothing pixel value is determined from the pixel value and pixel value of another image pixel of surrounding of the former image pixel. The latter pixel value is spaced apart from the former image pixel for averaging a distance weighting function. A pixel value weighting function and the distance weighting function are modified using an edge weighting function that is determined based on an edge strength of the former image pixel. Independent claims are also included for the following: (1) a computer program product comprising instructions to perform a method for bilateral filtering of digital image data (2) an image computer comprising instructions to perform a method for bilateral filtering of digital image data (3) a memory medium comprising instructions to perform a method for bilateral filtering of digital image data.

Description

The The invention relates to a method for bilateral filtering of digital Image data according to the preamble of claim 1, a corresponding Computer program product, storage medium and an image computer.

at many imaging methods, such. As the X-ray imaging, the tomographic Imaging, in particular computer tomographic imaging, In the image data, the image quality noise is included.

to Reduce noise and improve signal / noise ratio become the image data usually filtered by means of a filter. The filter should be in the Image data contained image-relevant structures at the same time high Noise reduction best possible receive. In particular, in the pictures contained edges and small, low-contrast structures are preserved.

For filtering, it is known to use so-called diffusion filters. A simple example of this is equivalent to linear Gaussian filtering. In addition, various extensions of the diffusion filter for edge-preserving noise reduction are also known. Such an extended method is for example off P. Perona and J. Malik, "Scale space and edge detection using anisotropic diffusion", IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 629-639, 1990 known.

Furthermore, methods are known in which an additional course of the edges is taken into account during the filtering. This is for example one J. Weickert "Anisotropic Diffusion Filtering in Image Processing", Teubner-Verlag, Stuttgart, Germany, 1998 known anisotropic filtering.

One The disadvantage of the diffusion filters is that the methods are carried out iteratively have to, consequently their implementation costly and for Medical image processing is not sufficiently powerful.

Out M. Elad "On the Origin of the Bilateral Filter" Ways to Improve It ", IEEE Transactions On Image Processing, Vol. 10, pp. 1141-1151, October 2002 It is known that there are non-iterative methods that are closely linked to non-linear diffusion filtering. Noniterative methods for edge-preserving noise reduction are also known by the term "bilateral filtering".

at In bilateral filtering, the image data is rendered nonlinear weighted averaging of pixel values locally smoothed. For weighting is a Distance weight function used, which has a geometric proximity of respective Picture pixels of the picture taken into account, which is also known under the term "Domain Filtering". Further For example, a pixel value weight function is used which has a photometric similarity the pixel values, e.g. B. a similarity of intensity values taking the pixel into account, which is also known by the term "range filtering".

One Disadvantage of this non-iterative procedure is that not with security It can be avoided that edges with a low signal / noise ratio are smoothed and defocus structures with low contrast. In strong Noise may cause the noise to be insufficiently removed becomes.

From that Based on an object of the invention, the disadvantages after to eliminate the prior art. It is intended in particular a method be provided, which is non-iteratively implementable. With In particular, it should be possible to use the method in the image data contained noise reliably remove, and at the same time edges and low-contrast structures to obtain. The method should also be particularly effective and with be comparatively low computational effort feasible. Another goal is it a computer program product as well as an image calculator for execution of the method.

These Task is solved by the features of the claims 1, 9 and 11. Embodiments emerge from the claims 2 to 8th.

To proviso The invention provides that the distance weight function and / or the pixel value weight function by means of a basis an edge thickness of the first image pixel determined edge weight function opposite to edge thickness be modified / will. The edge weight function may change depending on the implementation in the distance weight or pixel weight function same or opposite to the edge strength Behave the first image pixel.

By the modification can / can the distance weight function and / or pixel value weight function near be attenuated an edge contained in the image data. This may cause the smoothing in the Area of edges can be reduced. In particular, in the field the edges average the second image pixels, that of the first image pixel are relatively widely spaced, and their second pixel values comparatively strongly different from the first pixel value, be attenuated, and thus the smoothing. In areas without edges, z. B. in homogeneous image areas, can a reinforced one smoothing be achieved. It can an excellent noise reduction with the best possible preservation of the edges and low-contrast structures. In the By the way, averaging can be done to act on a non-linear averaging.

The Procedure can be implemented non-iteratively. This can the procedure can be done quickly and effectively. In particular it possible the method on distributed systems, z. A distributed computer network, or on special hardware, such as eg. FPGAs (Field Programmable Gate Array) or GPUs (Graphics Processing Unit), whereby a particularly effective and fast implementation can be achieved.

If the distance weight function and / or pixel weight function z. B. in each case by a Gaussian function with standard deviations σ _d or σ _r , the modification can be carried out by weighting the standard deviations σ _d or σ _r with the edge weight function.

The Edge weight function, for example, based on a Edge filtering or edge detection are determined in which for determining the edges of the image data on a first derivative a Gaussian function based filter core, also "Derivative of Gaussian "or called DoG edge detector for short, is used. For this purpose, an edge image can be determined from the image data whose pixel values reflect the edge strength. The edge strength can based on a convolution of the first pixel value with the first one Derivation of the Gaussian function be determined. The edge image can be timed before, in parallel and independently of the method according to the invention, on a distributed system or special hardware, which allows a particularly fast implementation of the method.

The Edge weight function can be the smaller the amount the more noise in the image data in at least one environment of the first image pixel is included. The noise can be used as a parameter considered become. As a parameter z. For example, the standard deviation of noise be used.

Especially It is advantageous if the distance weight function the second Pixel values regarding one the edge strength of the first image pixel reproducing gradient vector further weighted anisotropically, wherein for equally spaced from the first image pixel and starting from the first image pixel Image pixels in a direction parallel or perpendicular to the gradient vector second image pixels have a minimum or maximum weight the respective second pixel values.

With the anisotropic weighting, it is possible to use second image pixels along the edges stronger to weight than across the edges. This may cause the noise to go along the edges effectively suppressed be without the quality the edges prevail to impair. This means that in all image areas a high noise reduction at simultaneous preservation of the edges and structures can.

The inventive method can count on the pixel values or the smoothing pixel values several times in succession which achieves even better noise suppression can be. It should be emphasized that it is not mandatory is to execute the procedure iteratively.

To further requirement The invention provides a computer program product with program code means. which at execution on an image processor, the inventive method or one of its embodiments cause. Furthermore, a storage medium and image calculator with the Computer program product provided for carrying out the method. In terms of the benefits and benefits of the computer program product, Storage medium and image calculator will be on the designs to the method according to the invention and its embodiments referenced.

following Be exemplary embodiments of the invention explained in more detail with reference to FIGS. Show it:

1 a schematic flow diagram of the method according to the invention,

2 a digital original image with noisy image data,

3 an edge image of the original image,

4 the filtered with the inventive method original image of 2 .

5 the filtered with an embodiment of the inventive method original image of 2 .

6 the original image filtered by a prior art method 2 .

7 an enlarged portion of the filtered original image of 5 and

8th an enlarged portion of the filtered original image of 6 ,

1 shows a schematic flow diagram of the method according to the invention. This flowchart will be described below with reference to a filter F specified concretely, whereby the method can of course also be used in an analogous manner with other filters F.

Starting point of the procedure are image data of a like in 2 illustrated original image. The original image contains homogeneous image areas 1 and edges 2 , which in turn structures 3 with homogeneous image areas 1 surround. The homogeneous image areas 1 , Edge 3 and structures 3 are in 2 not all designated for reasons of clarity. Pixel coordinates (x, y) of the image pixels are indicated on the abscissa or ordinate axis y-.

Starting from the original picture of the 2 First, an edge thickness edge (x, y) of the first image pixel is determined. An edge image reproducing the edge strength edge (x, y) is in

3 represented, wherein the edge strength edge (x, y) increases with increasing gray value.

gefaltet, wobei σ_d weiter unten näher beschrieben wird.To determine the edge strength edge (x, y), for example, a so-called "Derivative of Gaussian" edge filtering can be used. In this case, the first pixel values f (x, y) of the image data, both in the x-direction and in the y-direction, become the first derivative of the Gaussian function:

folded, where σ _d is described in more detail below.

wobei g_x(x,y) bzw. g_y(x,y) die Ableitung obiger Gaußfunktion in x- bzw. y-Richtung bedeuten. Anschaulich werden bei dieser Faltung mit g_x(x,y) bzw. g_y(x,y) die Gradienten der Pixelwerte der Bilddaten in x- bzw. y-Richtung ermittelt. Die Gradienten in x- bzw. y-Richtung bilden für das erste Bildpixel einen Gradientenvektor eines die Kantenstärke edge(x,y) beschreibenden Gradientenfelds.This calculates the edge strength edge (x, y) as follows:

where g _x (x, y) or g _y (x, y) mean the derivative of the above Gaussian function in the x and y directions respectively. Clearly, in this convolution, the gradients of the pixel values of the image data in the x and y directions are determined by g _x (x, y) or g _y (x, y). The gradients in the x or y direction form, for the first image pixel, a gradient vector of a gradient field describing the edge strength edge (x, y).

Based on the edge strength edge (x, y), an edge weight function weight (x, y) is determined. Preferably, the edge weight function weight (x, y) is calculated as follows:

there K is closer below Illustrated, essentially freely selectable Parameter.

As can be seen from the flowchart of 1 2, the edge weight function weight (x, y) forms the basis for a modification of a distance weight function c (ξ, η, x, y) and / or pixel value weight function s (f (ξ, η), f (b) used in a bilateral filtering. x, y)).

wobei gilt:

In the known methods of bilaterally filtering the image data, smoothing pixel values h (x, y) for the filtered image z. B. calculated as follows:

where:

undHere k (x, y) are a normalization factor, f (x, y) are first pixel values and f (ξ, η) second pixel values. C (ξ, η, x, y) and s (f (ξ, n), f (x, y)) is the distance weight function or pixel value weight function, which are preferably given by:

and

in the Generally, by the distance weight function c (ξ, η, x, y) the geometric proximity between the respective underlying first image pixel with the first one Pixel value f (x, y) and a second image pixel with a second pixel value f (ξ, η) takes into account. With the pixel value weight function s (f (ξ, η), f (x, y)), there is a similarity between the first pixel value f (x, y) and the second pixel value f (ξ, η), e.g. B. a photometric similarity of intensity values the first f (x, y) and second pixel values f (ξ, η), respectively.

In the arguments of the distance weight function c (ξ, η, x, y) or pixel value weight function s (f (ξ, η), f (x, y)) the distance operator d (,) is used, with which in the present case the Euclidean Distance between first coordinates (x, y) of the first image pixels and second coordinates (ξ, η) of the second image pixels or the photometric difference or intensity difference between the first pixel values f (x, y) and the second pixel values f (ξ, η) can be determined. σ _d describes a geometric extension of the filter F, whereas σ _{r describes} its photometric expansion. With increasing σ _d , second image pixels in the vicinity of the first image pixel are increasingly weighted more and more. This means that the image data will be smoothed out more. As σ _r increases, second pixel values f (ξ, η) are increasingly taken into account, whose photometric similarity becomes increasingly different from the first pixel value f (x, y). The latter leads to a softening of the edges 2 and usually to the loss of image-relevant information, especially about low-contrast structures.

The previously described bilateral filtering for determining the smoothing pixel values h (x, y) corresponds, as explained above, to the filtering according to the prior art, the result of which in FIG 6 is shown. A comparison of 2 with the 6 and 8th shows that the filtering according to the prior art is only partially able to suppress the noise in the image. It can also be seen that the filtering leads to a significant softening of the edges 2 leads.

To avoid these problems according to the prior art, the solution according to the invention provides that the distance weight function c (ξ, η, x, y) and / or the pixel value weight function s (f (ξ, η), f (x, y)) is modified with the above-described edge weight function weight (x, y). A modification may be, for example, that σ _{r is} weighted with the edge weight function weight (x, y).

With increasing edge strength edge (x, y), the edge weight factor weight (x, y) becomes smaller in absolute value and thus also weight (x, y) · σ _r . As a result, fewer and fewer image pixels in the vicinity of the respective first image pixel are taken into account in the filtering, ie the geometric extent of the filter F is limited. This means in particular that the smoothing according to the edge strength edge (x, y) at the edges 2 is restricted, so that a softening of the edges 2 be avoided can. The quality of the edges 2 can be maintained and in the homogeneous image areas 1 a high noise reduction can be achieved, resulting from a comparison of the images of the 2 and 4 is apparent. It can also be seen that the edges 2 in accordance with the invention filtered original image of 4 less softened than the original image filtered by conventional filtering, without modification of the distance weight function c (ξ, η, x, y) 6 ,

Instead of σ _d , or in addition to it, σ _r can also be modified. The modification of the distance weight c (ξ, η, x, y) and / or pixel value weight function s (f (ξ, η), f (x, y)) can be arbitrary and is not limited to the above-described embodiment. Also conceivable is an immediate weighting of the distance weight c (ξ, η, x, y) and pixel value weight function s (f (ξ, η), f (x, y)) with one based on the edge weight function weight (x, y) determined any locally adaptive function.

Of the As has already been mentioned above, parameter K can essentially be chosen arbitrarily become. The parameter K can be used to influence the weighting and thus the smoothing become. A possible Measure of the parameter K can, for example, on the basis of an approximation of Noise can be determined in the original image. As value for the parameter K can z. The estimated Standard deviation of the noise can be used in the original image. This can be greater than in image areas with contrast / noise ratio One the strength the filtering caused by the smoothing in an advantageous manner influenced, in particular edge-sustaining be weakened.

With the above-described bilateral filtering according to the invention, which is modified according to the distance weight function c (ξ, η, x, y), it is possible in homogeneous image areas 1 ie in areas without edges 2 to achieve excellent noise reduction and smoothing while the edges 2 maintained in an advantageous manner with high quality. It should be noted that the Gaussian functions given above for the distance c (ξ, η, x, y) and pixel value weight function s (f (ξ, η), f (x, y)) are merely non-limiting examples.

In a development of the above exemplary embodiment, the profile of the edges is additionally filtered 2 considered. In this case, the distance weight function c (ξ, η, x, y) is modified by means of a further edge weight function describing the edge strength edge (x, y) of the first image pixel such that second image pixels along the edges 2 be weighted more heavily than across the edges 2 , This allows anisotropic filtering, ie the noise can travel along the edge 2 be suppressed while crossing the edge 2 the filtering is suppressed.

following becomes anisotropic according to the invention formed further distance weight function c '(ξ, η, x, y) described.

First, will based on the components of the gradient vector determined as described above Tensor D determined. This tensor D becomes a covariance matrix for the others From stand-weight function c '(ξ, η, x, y) used, which is preferably a multivariate Gaussian function is.

The tensor D can be chosen as follows:

Here, ν _{1 is} a normalized vector perpendicular to the gradient vector, ie locally parallel to the edge, and ν _{2 is} a normalized vector parallel to the gradient vector, ie locally perpendicular to the edge, and λ ₁ and λ ₂ are essentially freely selectable parameters. For the above tensor D, the condition λ ₁ = 1 means, for example, that along the edge 2 a smoothing of the image data is allowed. The parameter λ ₂ can be used to determine how much over the edge 2 smoothed away.

Preferably, the parameter λ ₂ for the respective first image pixel is determined as a function of its edge strength edge (x, y) as follows:

wobei D^–1 invers zum Tensor D ist.Using the tensor D, the further distance weight function c '(ξ, η, x, y) has the following form:

where D ^{-1 is} inverse to the tensor D.

5 shows the original image filtered using the anisotropic distance weight function c '(ξ, η, x, y). A comparison of 4 and 5 shows that in 4 along the edges 2 still contained noise in 5 is much lower. This means that with the inventive local adaptive anisotropic bilateral filtering the edges 2 at the same time high noise reduction, especially along the edges 2 , much better preserved. It should be noted that the method can be referred to as locally adaptive because the distance weight function c (ξ, η, x, y) or further distance weight function c '(ξ, η, x, y) and / or possibly also the Pixel value weight function s (f (ξ, η), f (x, y)) depend on the - local - edge strength edge (x, y) of the respectively considered first image pixel.

The advantages of the locally adaptive anisotropic bilateral filtering occur in a comparison of the 7 and 8th even clearer. 8th is a section of the original image filtered with non-local adaptive and non-anisotropic filtering 2 , 7 is a corresponding section of the original image filtered with the locally adaptive anisotropic filtering of the present invention 5 , It can be clearly seen that in the section of the 7 both in homogeneous image areas 1 as well as along the edges 2 much less noise is included. Further, the structures 3 , especially those with low contrast, such. For example, the roughly circular structure contained in the lower center of the image is significantly sharper. It also turns out that with the method according to the invention overlapping structures 3 can be separated much better.

In summary let yourself hold on to that with the locally adaptive and locally adaptive anisotropic Filtering excellent noise reduction while maintaining the edges can be reached. This can be avoided receive the best possible information contained in the original image stay. This relevant information, such as. B. small or low-contrast Structures or overlapping areas the structures are in pictures for medical diagnostic Purposes for safe diagnoses of considerable importance. It means that in the latter context, medical diagnoses on the basis of the filtered according to the invention Images can be created particularly secure.

The Application of the method according to the invention is not limited to medical image data, but to any Image data of any source applicable. Without limitation of Generality come digital image data or digital image data digitized images, by way of example as sources: Pictures of cameras or digital cameras, x-rays, tomographic Images, in particular images of X-ray computed tomography, magnetic resonance tomography, Ultrasound tomography, or other spectroscopic or tomographic Method.

One Another advantage of the method according to the invention in comparison to conventional Procedure is that an iterative implementation is not mandatory is. The inventive method can be applied several times in succession, but in emphasizes again that an iterative implementation is not mandatory. This makes the process particularly fast and executed effectively become. Because of this, the method is ideal for Implementation in special hardware, such as For example, FPGAs or GPUs. From that aside allows the inventive method unlike traditional ones non-linear adaptive filters provide efficient anisotropic filtering.

Next the above-described application of the method according to the invention in two-dimensional images can in an analogous way also three-dimensional images are filtered being for three-dimensional images the same advantages and advantageous Effects can be achieved.

Claims (11)

A method for bilaterally filtering digital image data of a digital image by means of a bilateral filter, wherein - for a first pixel value (f (x, y)) of a first image pixel of the image data, a smoothing pixel value (h (x, y)) is determined, wherein - the smoothing pixel value (h (x, y)) from the first pixel value (f (x, y)) and second pixel values (f (ξ, η)) second image pixels of an environment of the first image pixel is determined by weighted averaging, wherein For averaging, a distance weight function (c (ξ, η, x, y)) with which second pixel values (f (ξ, η)) are weighted the more, the less they are spaced from the first image pixel, and / or a pixel value weight function ( s (f (ξ, η), f (x, y))) is used with which second pixel values (f (ξ, η)) are weighted the more, the less the second pixel value (f (ξ, η)) from the first pixel value (f (x, y)), characterized in that - the distance weight function (c (ξ, η, x, y)) and / or the pixel value weight function (s (f (ξ, η), f (x, y))) are modified in opposite directions to the edge strength (edge (x, y)) by means of an edge weight function (weight (x, y)) determined on the basis of an edge thickness (edge (x, y)) of the first image pixel. becomes. The method of claim 1, wherein for determining the edge thickness (edge (x, y)) edge filtering is performed with a filter kernel, which corresponds to a first derivative of a Gaussian function. Method according to claim 2, wherein the edge strength (edge (x, y)) based on a convolution of the first pixel value (f (x, y)) the first derivative of the Gaussian function is determined. Method according to one of claims 1 to 3, wherein the edge weight function (weight (x, y)) the smaller the amount of noise in at least one environment of the first image pixel in the image data is included. The method of claim 4, wherein the noise is through its standard deviation in the edge weight function (weight (x, y)) considered becomes. Method according to one of claims 1 to 5, wherein the distance weight function (c (ξ, η, x, y)) the second pixel values (f (ξ, η)) with respect to a the edge strength (edge (x, y)) of the first image pixel reproducing gradient vector further weighted anisotropically, being equal to from the first image pixel spaced and starting from the first image pixel in one direction parallel or perpendicular to the gradient vector located second image pixels a minimum and maximum weight of the respective second pixel values (f (ξ, η)) takes place. Method according to one of claims 1 to 6, wherein for the determination the edge weight function (edge (x, y)) an edge image of the image data is determined. Method according to one of claims 1 to 7, which several times successively to the first pixel values (f (x, y)) or smoothing pixel values (h (x, y)) is applied. Computer program product with program code means, which at execution on a picture computer a method according to one of claims 1 to 8 effect. Image calculator with a computer program program product stored thereon according to claim 9. Storage medium with a computer program program product stored thereon according to claim 9.