WO2006032855A2 - Ameliorations apportees au traitement d'images - Google Patents

Ameliorations apportees au traitement d'images Download PDF

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Publication number
WO2006032855A2
WO2006032855A2 PCT/GB2005/003592 GB2005003592W WO2006032855A2 WO 2006032855 A2 WO2006032855 A2 WO 2006032855A2 GB 2005003592 W GB2005003592 W GB 2005003592W WO 2006032855 A2 WO2006032855 A2 WO 2006032855A2
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Prior art keywords
image
local
window
phase
orientation
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PCT/GB2005/003592
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English (en)
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WO2006032855A3 (fr
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Matthew Mellor
John Michael Brady
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Isis Innovation Limited
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Publication of WO2006032855A3 publication Critical patent/WO2006032855A3/fr

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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T7/00—Image analysis
    • G06T7/30—Determination of transform parameters for the alignment of images, i.e. image registration
    • G06T7/35—Determination of transform parameters for the alignment of images, i.e. image registration using statistical methods
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T7/00—Image analysis
    • G06T7/30—Determination of transform parameters for the alignment of images, i.e. image registration
    • G06T7/33—Determination of transform parameters for the alignment of images, i.e. image registration using feature-based methods
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T2207/00—Indexing scheme for image analysis or image enhancement
    • G06T2207/30—Subject of image; Context of image processing
    • G06T2207/30004—Biomedical image processing

Definitions

  • the present invention relates to image processing and, in particular, to improvements in techniques for "registering” or aligning as accurately as possible two or more images with each other.
  • the need to align two (or more) images arises in a variety of imaging fields.
  • images of the same patient taken with different modalities for example MRI, CT, PET
  • images taken at different times to monitor the development of some condition or disease.
  • a similar requirement occurs when an image of a patient is to be compared with a standardized image-like model known as an atlas.
  • the need for image alignment also occurs in other fields.
  • Image alignment may also be required in analysis of image motion: in the computation of the optic flow or the estimation of three-dimensional structure from motion. Also, in the case of multi-view image analysis such as stereo vision, the simultaneously-taken images from two or more cameras need to be aligned and combined to form an estimate of the three-dimensional locations of points in the scene.
  • image alignment techniques have proceeded by taking the two image data sets, applying some form of transformation to one of them (such as a rigid transformation involving displacement and rotation, or a non-rigid transformation including, for example, warping of the structures), calculating the similarity between one of the data sets and the transformed version of the other data set, and adjusting the transformation, usually iteratively, to attempt to minimize the difference.
  • some form of transformation such as a rigid transformation involving displacement and rotation, or a non-rigid transformation including, for example, warping of the structures
  • the mutual information of the intensities of two images, / Wenn & /, can be defined in terms of the probability distributions of the intensities of the individual pixels as follows :-
  • step 13 it is checked whether the images are sufficiently aligned and, if not, the transformation is changed slightly in step 14 and steps 11 and 12 are repeated. This continues iteratively until the similarity measure has reached the required value, or, for example, has not changed significantly with the change in the transformation, at which point the process ends at step 15 with the value of the transformation which gives the best alignment having been calculated.
  • one way of allowing for noise in the image is to use a windowing technique in the calculation of the probability distribution mentioned above.
  • preparing an individual probability distribution of the intensities in an image simply involves preparing a histogram of those intensities (with each intensity value contributing only to one bin of the histogram) where a windowing technique is used, each intensity value contributes not only to its "primary" bin, but also partially to neighbouring bins.
  • the amount of contribution to neighbouring bins depends on the noise model chosen. For example, if a Gaussian noise model is chosen, each observed intensity value is regarded as forming the center of a Gaussian distribution, with the contribution to neighbouring histogram bins corresponding to the values of the Gaussian distribution.
  • image applies not only to values of intensities calculated in two spatial dimensions, but also to image sets which are in three dimensions (in which case the pixels are usually known as voxels) and also to two or three dimensions plus time, hi the present specification, though, the term “image” will be regarded as covering all such data sets, and the term “pixels” will be used to include "voxels”.
  • a first aspect of the present invention relates to the use of a new image descriptor for image alignment.
  • This image descriptor consists of one or more of the local energy, local phase and local orientation in the image.
  • the local energy, local phase and local orientation are values which can be calculated from the intensity values in an image. These are values which describe the structure in the image.
  • One definition of energy, phase and orientation is known as the monogenic signal, as discussed, for example, in "Low- Level Image Processing with the Structure Multivector", M. Felsberg, PhD thesis, Christian- Albrechts-Universitat Kiel, 2002 http://www.isy.liu.se/ ⁇ mfe/Diss.ps.gz.
  • the analysis is conducted on an image descriptor comprising one or more of these values.
  • the analysis is conducted at a plurality of different scales.
  • Each of local energy, local phase and local orientation presuppose analysis of the image at a certain scale. Images may be aligned more quickly by starting the analysis at a relatively large scale (this may correspond, for example, to aligning the overall outline of two image structures), followed by analysis at successively smaller scales. It should be noted, as mentioned above, that the scales may be purely spatial or temporal.
  • a second aspect of the invention relates to an adaptation of the way in which the probability distributions of the image descriptor are calculated in order better to account for the noise in the image.
  • a windowing function is used when calculating the probability distributions and the size and shape of the window are varied in accordance with the local structure in the image.
  • the size and shape of the window can be varied in accordance with the local energy as calculated at each position in the image. Preferably the greater the local energy the smaller the windo ⁇ v. This reduces the susceptibility of the joint probability distribution estimate to the effects of noise.
  • the method becomes feature driven (ie. features in the image are used preferentially in the alignment process as the contribution to the histograms in these areas is less "smeared out").
  • the aspects are combined together so that the image descriptor consisting of one or more of the local energy, local phase and local orientation is used as the image descriptor in the calculation of the probability distributions using an energy-dependent window as mentioned above .
  • Figure 1 is a flow diagram illustrating the general technique of image alignment used in the prior art
  • Figure 2 is a flow diagram illustrating the general image alignment method in accordance with an embodiment of the present invention.
  • FIG. 3 illustrates schematically the calculation of the image descriptor in accordance with one embodiment of the present invention
  • Figure 4 illustrates schematically the calculation of the probability distribution of image descriptors in accordance with an embodiment of the present invention
  • Figures 5 A to I are flow diagrams and pseudo-code schematically illustrating an example of the present invention.
  • FIGS 6 (a) to (d) illustrate an example of image alignment using an embodiment of the present invention.
  • step 20 the two sets of image data to be aligned or "registered" are received. As discussed above, these may be two-dimensional images or three-dimensional images, and may be supplemented by time.
  • step 21 one or more scales are chosen for the image analysis. Preferably a multi-scale approach is used, with the analysis first being conducted at a relatively large scale, and then successively smaller scales (corresponding to finer resolutions). In the example which is illustrated in Figure 6, four different scales were chosen. The scales are chosen based on the size of the structures in the image and the accuracy of the registration required.
  • the monogenic signal is calculated for each image point at the chosen scale.
  • the monogenic signal consists of the local energy, the local phase and the local orientation.
  • Methods of calculating the monogenic signal are known, and any of the available techniques may be used with the present invention, for example steerable quadrature filters such as described in "The Design and Use of Steerable Filters” by Freeman and Adelson (PAMI 13(9), Sept 1991, S91-906) or by the techniques described in "Low- Level Image Processing with the Structure Multivector", M. Felsberg, PhD thesis, Christian- Albrechts-Universitat Kiel, 2002 http://www.isy.liu.se/ ⁇ mfe/Diss.ps.gz. This is discussed in more detail below.
  • the candidate transformation is applied to one of the data sets and in step 24 the probability distributions needed for calculation of the similarity measure in step 25 are calculated.
  • the probability distributions are calculated taking into account the noise in the image in an adaptive way in accordance with the local structure in the image. Further, they are calculated on the components of the monogenic signal - the local energy, local phase and local orientation, not on the intensities as in the prior art.
  • Step 26 and 27 correspond to the normal iterative processing to optimize the transformation and in step 28 it is checked whether all scales have been completed. If not then steps 22 to 26 are repeated for each of the chosen scale until they are all completed, at which point the process ends at step 30 with best estimate for the transformation havin ⁇ tog been calculated.
  • the local energy, local phase and local orientation are indicative of the local properties of a region within an image. For example, they describe such features as step changes, ridges, sudden spikes and so on.
  • Image features can be classified according to their local symmetry. Just as any real signal can be locally decomposed into a symmetric part and anti-symmetric part (corresponding, for example, to the sine and cosine Fourier components), the same is true of image features. For example, an edge between a dark area and a light area is locally anti-symmetric while a peak in intensity is locally symmetric.
  • the ratio of the amplitude of the symmetric and anti-symmetric components in any given feature amounts to a simple summary of the local shape of the intensity profile of the feature.
  • the combined amplitude gives information about the amount of local signal activity, and reaches a local maximum near the center of the feature. These two quantities are what is measured by the phase and energy in the monogenic signal respectively. If considering, therefore, the variation of intensity across an image feature such as an edge from white to black, this feature is locally anti-symmetric and so could be described as having mainly a sine component and thus a phase close to say, zero. On the other hand, a feature which is symmetric (and thus over the same distance goes from white to black and white again) would have predominantly a cosine component and thus a phase of nearer ninety degrees.
  • the phase and energy can be obtained from an image data set by convolving it with a pair of quadrature filters, but with a two (or more) dimensional image there is the problem that the image features are different in different directions across the image.
  • the monogenic signal also includes the feature orientation which can intuitively be understood as the direction associated with a local linear structure (such as the direction of an edge).
  • the three quantities of local phase, local energy and local orientation can be obtained by using three filters which are convolved with the image, using the known techniques described in the references above.
  • Figure 3 illustrates this schematically in which two odd filters, one for the vertical direction in the image and one for the horizontal direction, and one isotropic even filter are used and their outputs are combined to calculate the three components of the monogenic signal: the local energy A s , the local phase ⁇ and the local orientation ⁇ .
  • the intensity values are converted into values at each image point (pixel) for the components of the monogenic signal - the local energy, the local phase and the local orientation.
  • the next step involves calculating the individual probability distributions in the two data sets, and also the joint probability distribution corresponding to steps 23 and 24 of Figure 2.
  • a conventional way of estimating a probability distribution taking account of noise is to use a windowing function, such as a Parzen window in the construction of the histogram or joint histogram.
  • a windowing function such as a Parzen window in the construction of the histogram or joint histogram.
  • each value being added to the histogram contributes not to a single bin, but contributes over several bins in a distribution which is based on the noise model for the data set.
  • the distribution would be: -
  • ⁇ is the standard deviation of the noise.
  • this equation tells you how much of the vote of observed signal h goes into each bin / of the histogram.
  • this equation is used to calculate the contribution at each image point in the same way.
  • this windowing function is adjusted at each point in accordance with the local image structure, hi this embodiment it is adjusted by the local energy A k at that point so that, for example, taking the phase component of the monogenic signal, the Parzen window is defined as:-
  • the histogram bin for phase value ⁇ receives the value calculated by equation 2 where A 1 is the local energy (also calculated from the monogenic signal), and ⁇ is the standard deviation of the noise model, which is estimated for each image data set, for example by modelling the imaging process or by calculating the variance of the intensity in the image. So the amount of "smearing" of the observed values represented by the windowing function varies from point to point in the image with the local energy. In essence, ⁇ , which governs the size and shape of the window, is modified by the local energy, which is an aspect of image structure.
  • a 0 is the odd component of the energy, calculated as the square root of the sum of the two odd parts of the monogenic signal at each scale.
  • Figure 4 illustrates schematically how the probability distributions for the components of the monogenic signal are calculated.
  • a linear noise model 40 (for example the Gaussian noise model discussed above or any other noise model suitable for the image data set) is convolved with the same filters 41 , 42 and 43 to generate the monogenic signal and is then utilized in the estimation at 44, 45 and 46 of the probability distribution functions 44, 45 and 46 for the local energy, local orientation and local phase.
  • Figure 6 illustrates an example of two test images to which the present invention was applied.
  • Figure 6a and Figure 6b illustrate two significantly different images of the same scene.
  • Figure 6c illustrates the most likely horizontal alignment of the two images as calculated by the use of traditional mutual information of the intensities in the two image data sets. It can be seen that there is a peak at zero, implying that the images should be aligned at this point.
  • Figure 6d illustrates the correct alignment point as calculated using an embodiment of the present invention.
  • the method of Figure 2 was run at four different scales and assuming a simple white, additive Gaussian noise model. It can be seen that again there is a peak at zero, illustrating that the correct alignment was calculated, but that this peak is much clearer than the peak in Figure 4c.
  • FIG. 5 A illustrates the overall process.
  • the images are received in step 50 and approximately aligned (e.g. by rigid registration algorithm as known in the art (not illustrated in Figure 5A)).
  • One image is designated the source image and the other the target image.
  • the source image will be deformed until it is aligned with the target image.
  • Local energy, local phase and local orientation are then calculated at step 51 (in process A which will be described in more detail below) for each image, at a particular scale, which may be chosen by the designer to suit the problem at hand.
  • step 52 the initial joint Probability Distribution (PDF) of the descriptors must be estimated, for example using process B as shown by the pseudocode in Figure 5F.
  • step 53 the incremental improvement to the transformation is calculated, for example by process C shown in Figures 5 G to 51 and the new transformation is applied to the source image. This process is continued iteratively until the improvement DF in alignment caused by the change to the transformation is less than a threshold lim as tested at step 55, finishing at step 56 with the best alignment achieved.
  • PDF Probability Distribution
  • process A local energy, local phase and local orientation are calculated from the response of a set of three filters at each scale, as shown in figures 5C, 5D and 5E.
  • the choice of the filter family is application specific; in this example a family of non-blurring filters are used.
  • the overall flow is shown in Figure 5B.
  • N is five in this example, a set of three filters is constructed in step Al.
  • the rotationally symmetric filter is defined.
  • the odd filter responses are calculated from the band ⁇ pass filtered images.
  • each of the bandpass filters is convolved with each of Hi and H2 to form the odd filtered images, as in step
  • Odd_l _x sca ⁇ e convolve(Bandpass_l Sca i e ,Hl) and the three subsequent steps. Finally, the local energy and local phase may be calculated, as in figure 5E.
  • the next step in the registration procedure is to estimate the joint PDF, as shown in figure 5F.
  • the descriptor will consist of only the local phase.
  • the first step in estimating the joint PDF is to define an image noise model; typically this might be Additive White Gaussian distributed Noise (AWGN). This only needs to be defined once, at the beginning of the process, and may be obtained, for example, from a prior knowledge of the noise characteristics of the imaging apparatus.
  • AWGN Additive White Gaussian distributed Noise
  • the PDF is initialised, hi the present example, the PDF is represented by a two dimensional histogram of ten thousand bins (one hundred bins square), initialised to zero.
  • the final step is to calculate the first and second marginal distributions by summing the PDF along for all values of first and second phase respectively, which is accomplished by the final two lines in the outer loop of figure 5F.
  • the function roundQ rounds its argument to the nearest integer value and the factors 198 and pi are chosen to guarantee that the resulting index value lies somewhere in the interval 1 to Binjio.

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Abstract

La présente invention concerne un procédé de calage des images telles que les images multimodales, et notamment les images entachées de bruit. En l'occurrence, on commence par convertir en énergie locale, phase locale et orientation locale les intensités des images pour donner un descripteur d'image tenant compte de la structure d'image. Sur ce descripteur d'image, on effectue des calculs de distributions de probabilités et de similitudes. Les calculs de distributions de probabilités peuvent comporter un mise en fenêtre avec une fenêtre dont les dimensions et la forme sont fonction de l'énergie locale dans l'image.
PCT/GB2005/003592 2004-09-21 2005-09-19 Ameliorations apportees au traitement d'images WO2006032855A2 (fr)

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Cited By (3)

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Publication number Priority date Publication date Assignee Title
CN102034227A (zh) * 2010-12-29 2011-04-27 四川九洲电器集团有限责任公司 一种图像去噪的方法
GB2477183A (en) * 2009-12-21 2011-07-27 Siemens Medical Solutions Processing medical imaging data using phase information
CN104299235A (zh) * 2014-10-10 2015-01-21 中国科学院长春光学精密机械与物理研究所 基于面积积分式的配准描述子方向计算方法

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Cited By (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
GB2477183A (en) * 2009-12-21 2011-07-27 Siemens Medical Solutions Processing medical imaging data using phase information
GB2477183B (en) * 2009-12-21 2014-08-13 Siemens Medical Solutions Methods and apparatus for processing medical imaging data using phase information
CN102034227A (zh) * 2010-12-29 2011-04-27 四川九洲电器集团有限责任公司 一种图像去噪的方法
CN104299235A (zh) * 2014-10-10 2015-01-21 中国科学院长春光学精密机械与物理研究所 基于面积积分式的配准描述子方向计算方法
CN104299235B (zh) * 2014-10-10 2017-06-13 中国科学院长春光学精密机械与物理研究所 基于面积积分式的配准描述子方向计算方法

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