WO2008012754A2

WO2008012754A2 - Volumetric data projection

Info

Publication number: WO2008012754A2
Application number: PCT/IB2007/052913
Authority: WO
Inventors: Roel Truyen; Patrik Rogalla; Henning Meyer
Original assignee: Koninklijke Philips Electronics N.V.
Priority date: 2006-07-25
Filing date: 2007-07-23
Publication date: 2008-01-31
Also published as: WO2008012754A3

Abstract

A system and method for computing a projection image from a volume data set, in particular a medical imaging volume data set, involving determining 502 a plurality of rays intersecting the volume. Each ray 504 is associated with a respective pixel in a projection plane. For each ray 504, a plurality of intensity values is collected 504 associated with voxels in a neighborhood of the ray. Each weight of a plurality of predefined weights is associated 508 with a respective intensity value of the plurality of intensity values in dependence on an ordering of the plurality of intensity values with respect to intensity. At least two weights of the plurality of weights are nonzero and at least two weights of the plurality of weights have a mutually different value. A weighted sum 510 of the intensity values is computed using the associated weights. The outcome of the weighted sum is associated 512 with the respective pixel.

Description

Volumetric data projection

FIELD OF THE INVENTION

The invention relates to computing a projection image from a volume data set, in particular a medical imaging volume data set.

BACKGROUND OF THE INVENTION An important visualization method in medical imaging is projection imaging.

A three-dimensional data set can be projected onto a two-dimensional plane for display. Volume data comprises a three-dimensional grid of volume elements called voxels. The voxels are assigned respective values representative of, for example, a measured local physical quantity within a patienf s body. Volume data is produced by, for example, computed tomography (CT) scanners or magnetic resonance imaging (MRI) scanners. Two-dimensional images comprise a two-dimensional grid of picture elements called pixels. Known projection methods analyze voxels along the projection direction and perform summation or averaging of voxels along a projection ray to obtain a pixel value of the projection. Other known methods find a maximum or minimum voxel value along the ray and assign the found value to the pixel value. While there is a good noise reduction in images resulting from summation or averaging, there is edge and contrast enhancement in images resulting from the minimum or maximum voxels.

US 5,297,551 discloses averaging or weighting of voxel values to compensate for whether the ray passes directly through a voxel or between two voxels. EP 0 621 546 discloses a way of determining the values of respective pixels by forming a weighted combination of respective intensity sums and respective maximum intensities of values along respective rays. Here, the intensity sums are formed by summing the intensities of voxels intercepted by or interpolated along respective parallel rays projected in a given direction through a depth-cued array of computed voxel intensities. The maximum intensities are determined of voxels intercepted by or interpolated along respective parallel rays associated with the respective pixels and directed in a given direction, as projected through a pre-MIP three-dimensional array of voxel intensities derived from an initial three- dimensional array. Said determining of the values of the respective pixels is by forming a weighted combination of said respective maximum intensities and said respective sums for the rays associated with the respective pixels.

The document also discloses a method for enhancing vessel visualization in the projection image comprising segmenting the voxels into flow voxels and background voxels; computing a low-pass filtered volume wherein the flow voxel values are replaced by an average voxel value of the background voxels; subtracting the original volume and the low-pass filtered volume; and intensity thresholding the subtracted volume to form a so- called pre-depth-cued array. Subsequent depth cueing is provided by applying a scale function having an intensity multiplying scale factor that monotonically increases over viewing distance in the viewing direction from back to front. Depth cueing is used to introduce a contrast whereby closer objects appear brighter than more distant ones.

SUMMARY OF THE INVENTION

It would be advantageous to have an improved system for computing a projection image from a volume data set, in particular a medical imaging volume data set. To better address this concern, in a first aspect of the invention a system is presented that comprises: means (702) for determining a plurality of rays intersecting the volume, each ray being associated with a respective pixel in the projection image; means (704) for collecting a plurality of intensity values associated with voxels in a neighborhood of a ray of the plurality of rays; means (706) for associating each weight of a plurality of predefined weights with at least one intensity value of the plurality of intensity values in dependence on an ordering of the plurality of intensity values with respect to intensity, at least two weights of the plurality of weights being nonzero and at least two weights of the plurality of weights having a mutually different value; means (708) for computing a weighted sum of the intensity values using the associated weights; and means (710) for associating an outcome of the weighted sum with the respective pixel.

It becomes possible to create a projection image that combines properties of average intensity projection and maximum intensity projection. It becomes possible to create projection images with enhanced edges combined with noise reduction. The weights may for example be optimized for specific types of medical images, such as angiographic images, images of certain organs, or images for diagnosing specific diseases.

According to an aspect of the invention, for any two intensity values of the plurality of intensity values, a first intensity value being smaller than a second intensity value, a weight is associated with the first intensity value that is smaller than or equal to a weight associated with the second intensity value.

According to an aspect of the invention, for any two intensity values of the plurality of intensity values, a first intensity value being smaller than a second intensity value, a weight is associated with the first intensity value that is greater than or equal to a weight associated with the second intensity value.

By assigning relatively smaller/greater weights to intensities being relatively small compared to the other intensities in a ray, the larger/smaller intensity values along the ray have a relatively large weight in the projection pixel value, which results in enhanced edges. In contrast to maximum/minimum intensity projection, many more than one intensity value is taken into account during the computation of the projection pixel value. This provides for the noise reducing averaging effect.

According to an aspect of the invention, the plurality of weights comprises a first sequence of linearly increasing weights and a disjunct second sequence of linearly increasing weights, where the first sequence increases with a different value than the second sequence.

Two sets of differently linearly increasing weights allow all intensity values to contribute to the pixel value while still preserving enhanced edges. The linearly increasing weights are simple to implement and need only little computational power.

In an embodiment, the plurality of intensity values are sorted according to the ordering to form a sorted list; and the step of associating the weights is performed based on a position of each intensity value in the sorted list.

This provides for a high level of customization. The weights may be computed each time according to a mathematical formula. Also, the weights may be pre-computed and stored in a list. One weight value may be computed once and stored for each position of the sorted list.

In an embodiment, a difference between any two weights associated with two successive intensity values in the list is fixed.

Linearly increasing weights are relatively simple to implement. In an embodiment, a difference between any two weights associated with two successive intensity values in a first portion of the list is equal to a first fixed value, and a difference between any two weights associated with two successive intensity values in a second portion of the list is equal to a second fixed value, the portions of the list being disjunct and both portions of the list consisting of a series of subsequent positions in the list.

BRIEF DESCRIPTION OF THE DRAWINGS

These and other aspects of the invention will be further elucidated and described with reference to the drawing, in which Fig. 1 illustrates MIP and average projection imaging;

Fig. 2 illustrates a projection method;

Fig. 3 shows three differently processed projection images;

Fig. 4 shows three differently processed projection images;

Fig. 5 illustrates a flow chart illustrating processing steps; Fig. 6 illustrates a flow chart illustrating processing steps; and

Fig. 7 is a diagram of an embodiment.

DETAILED DESCRIPTION OF EMBODIMENTS

Projections are a post processing method for digital imaging, especially CT and MR, which merge a volume slab into one slice. This can be useful because certain projections can enhance pathologic features in the image. Projections furthermore reduce the amount of images that need to be reviewed and reported, compared to viewing individual cross sectional slices of the volume.

Currently two important projections are used in digital imaging. In the average projection the resulting slice is calculated as the average of the source slab of the volume. In the Maximum intensity projection (MIP) each pixel of the resulting slice is calculated as the maximum value of the voxels along the ray of view of this pixel. Similarly, the minimum value of the voxels along the ray of view of the pixel can be computed. Minimum and maximum intensity projection have identical properties with respect to noise and edge enhancement. While there is a good noise reduction in images of average projection, there is edge and contrast enhancement in images of MIP.

In medical imaging, there is a tradeoff between on the one hand a low radiation exposure, short acquisition time, high spatial resolution, and/or a high temporal resolution, and on the other hand signal to noise ratio. Optimizing the first set of criteria is usually at the cost of the signal to noise ratio. This tradeoff negatively influences the diagnostic quality of the images. Since the MIP projection technique introduces more noise in the image, it is less suitable for images with a low signal to noise ratio.

Image quality of MIP and average projection is limited when applied to volumetric image data with high noise. Although noise reduction is still considered acceptable in average projection images, the images are relatively blurry and contrast and edge sharpness are reduced due to the averaging of all intensity values along a ray and also due to the partial volume effect.

MIP images may be considered nearly unusable in some image data with high noise, because image noise is enhanced by MIP. Although contrasts and edges are enhanced as well, this is of no benefit because of the high image noise.

Figure 1 illustrates MIP and average projection. The Figure shows a volume 100 consisting of a three-dimensional grid of voxels, a projection plane 104, and a ray 102 intersecting the volume 100 and the projection plane 104. The projection image consisting of a grid of pixels is illustrated as the projection plane 104. It is illustrated how intensity values along a line (ray) 102 through the volume 100 are processed to obtain a pixel value corresponding to the intersection point of the ray 102 and the projection plane 104. The Figure illustrates the average projection wherein intensity values of all voxels along the ray 102 are averaged (AVG) to obtain an average projection pixel value. It is also illustrated how the highest intensity value along the ray 102 through the volume 100 is used as the maximum intensity projection (MIP) pixel value.

Figure 2 illustrates an embodiment of the invention. It shows the volume 212, projection plane 214, and ray 210 intersecting the volume 212 and the projection plane 214, similar to Figure 1. The ray 210 is associated with a pixel at the intersection point of the ray 210 and the projection plane 214. Figure 2 shows that gray values or intensity values 200 associated with voxels in a neighborhood of a ray 210 (i.e., a line) through the volume are collected to obtain a plurality of intensity values 202. The values in the plurality of intensity values 202 are sorted according to intensity value to obtain a sorted list 204. The Figure also shows a graphical representation of a weighting function 206. It shows that weighting function 206 has relatively large values for relatively bright (or high) intensities and relatively small values for relatively dark (or low) intensities. This could also be the other way round, i.e., the weighting function could also have a large value for dark intensities. Other, non-monotonic intensity functions can also be used. This depends on the nature of the image and the requirements of the visualization. To compute a pixel value of the projection image, a weighted sum is computed as follows:

p(r) = ∑ w(n)I_r (n) , (1)

B-I where r denotes a particular ray intersecting the volume, p(r) denotes the projection pixel value 208 associated with ray r, n is an index value indicating an element of the (sorted) list 204 of intensity values, N is the number of elements in the (sorted) list 204, I_r{n) is element n of the sorted list 204 associated with ray r, and w(n) is the value of the weighting function 206 for element n of the sorted intensity vector.

In summary, the voxels of each ray are sorted first according to intensity value, for example in ascending order. After sorting the values of the voxels they are weighted according to a weighting function. The value of the resulting pixel is the sum of the weighted voxels.

Equation (1) is a generalization of average intensity projection and MIP, because setting

w(n) = — , n = l,... , N

N results in the known average intensity projection, and setting

results in the known maximum intensity projection (MIP).

The method may combine the advantages of both average projection and MIP, for example edges may be enhanced like in MIP images, and noise may be reduced like in average projection images.

In an embodiment, the weighting function associates a weight larger than 0 with at least one of the vector elements n different from N. This means that w(n) ≠ 0 for at least one n < N . Also, the weighting function associates an equal weight to at most N - I vector elements. This means that m and n exist with \ ≤ m < n ≤ N such that w(m) ≠ w(n) . By thus carefully selecting the weight function, a more subtle projection image is realized as compared to maximum and average intensity projection imaging. For example, setting f0 , n = l,... , N - 2 win) = <

U , n = N - \, n = N provides a high degree of contrast enhancement (compared to average projection) in combination with some noise reduction (compared to MIP).

In an embodiment, the weighting function w(n) is a non-decreasing function. Examples of suitable non-decreasing functions include

w(n) = and

^ N(N + V) 0 n = \,... , N - k w(n) = n - (N - k) n = N - k + \,... N. y *(* + !)

In these examples, the sum of all w(n) equals 1. This can be seen by making

N use of the fact that for any N ≥ 0 it holds that £n = { N(N + T) . Usually it will be preferred

B=I

to use a weighting function satisfying ^ w(n) = 1 , because in that case the weighted sum is

B=I in the same range of values as the intensity values in the volume. However, this is not required.

In an embodiment,

N

0.5^ n < —

2 w(n) = N

1.5^ - 0.5 n ≥ — .

N 2

In an embodiment,

1 n n < —N w(n) = 3 ΪV 4

3^ - 2 n ≥ -N.

N 4

Figure 3 and 4 show Ultra Low Dose CT images. Average projection images are shown on the left, MIP images are shown on the right, and projection images computed using (1) are shown in the middle. The differences in image quality can be seen.

Figure 5 illustrates an example control flow in an embodiment. It shows (in step 502) determining a plurality of rays intersecting a (medical) volume image data set. Each ray is associated with a respective pixel in a projection plane. For example, the projection plane comprises a rectangular grid of pixel values. The rays can be for example parallel to each other and perpendicular to the projection plane. The rays can also be defined as lines intersecting a given focal spot and given respective points on the projection plane for the respective pixels. The projection direction is arbitrary, i.e., the projection plane may have any orientation and the focal spot may have any position. Some of the rays associated with a pixel in the projection plane may not intersect the volume. Those rays are not considered here. They may be assigned a value of zero, for example. In step 504, one of the rays is selected that has not yet been processed. The following steps apply to this selected ray. In step 506, a plurality of intensity values are collected. The intensity values are associated with voxels in a neighborhood of the ray. For example, the intensity values associated with voxels intersected by the ray are collected. In another example, the volume is sampled at regular intervals along the ray. The intensity value at a sampling point may be computed by interpolating the intensity values of (for example) eight voxels closest to the sampling point. Tri- linear interpolation may be used as known in the art. A sampling point outside the volume may be given an appropriate value such as zero. A fixed number of intensity values may be collected for each ray, or different numbers of intensity values may be collected. The number of intensity values collected may depend on the length of the intersecting piece of the ray. In step 508, weights are associated with the collected intensity values. One weight value is associated with each intensity value. Preferably the sum of the weight values is the same for each ray. If the number of intensity values collected for each ray is variable, then the weights may be computed separately for each number of intensity values that occurs. For example, the exemplary equations defining w(n) presented above may be used with appropriate values of N. The weight values are associated with the intensity values in dependence on an ordering of the plurality of intensity values. For example, the greatest 10% of the intensity values may be associated with a relatively high weight and the smallest 90% of the intensity values may be associated with a relatively low weight. The exemplary equations defining w(n) presented above may also be used, where n denotes the n-th smallest intensity value or the n-th greatest intensity value. For example, at least two weights of the plurality of weights are nonzero and at least two weights of the plurality of weights have a mutually different value. In step 510, the weighted sum of the intensity values is computed using the associated weights according to Equation (1). The outcome of the weighted sum is associated with the respective pixel corresponding to the ray selected in step 504. The pixel value may be subject to further processing after having computed the weighted sum.

In step 514, it is checked if all rays have been processed, and if not, the next ray is selected by starting from step 504.

In an embodiment, it holds that if a first intensity value collected in step 506 is smaller than a second intensity value collected in step 506, the weight associated with the first intensity value is smaller than the weight associated with the second intensity value. In another embodiment, it holds that if a first intensity value collected in step 506 is smaller than a second intensity value collected in step 506, the weight associated with the first intensity value is larger than the weight associated with the second intensity value. Figure 6 illustrates an example control flow. In step 602, a ray through a volume is determined, the ray being associated with a pixel of a projection image. The way to establish such a ray is known in the art. In step 604, intensity values (or gray values) of voxels along the ray are collected, for example by collecting voxel values of all voxels intersected by the ray. Another way of collecting the values is by interpolating intensity values of voxels in a neighborhood of the ray. Such interpolation techniques are known in the art. The collected intensity values are sorted in step 606. In step 608, a weighted sum of the sorted intensity values is computed. In step 610, the weighted sum is assigned to the pixel corresponding to the ray. If a value has been assigned to each pixel in step 612, the projection image is completed. Otherwise, control continues from step 602 with the ray associated to a different pixel.

Figure 7 illustrates an embodiment of the invention. The Figure shows a system, for example a medical workstation, with a processor 722 and memory 721. The memory 721 contains instructions for causing the processor to perform the method set forth. In particular, it contains instructions 702 for determining a plurality of rays intersecting the volume and the projection plane, each ray being associated with a respective pixel in the projection plane. Memory 721 also comprises instructions 704 for collecting a plurality of intensity values along the ray. Memory 721 also stores instructions 706 for causing the processor 722 to associate the weights to the respective intensity values as set forth, instructions 708 for computing the weighted sum, and instructions 710 for associating the weighted sum with the respective pixel. It will be understood that one or more of the blocks 702-710 may also be implemented as hardware components, preferably under control of processor 722. The memory 721 also contains collected intensity values and projection image pixel values. The Figure also shows communication port 725 for receiving volume image data and/or transmitting projection image data via a network such as a TCP/IP or Wifi network. The Figure also shows removable media 726 that can also be used for storing the volume and/or projection data. The input means 724 can comprise a computer mouse and/or keyboard for allowing a user to operate the system. The display 723 is used for rendering the projection image. It will be appreciated that the invention also extends to computer programs, particularly computer programs on or in a carrier, adapted for putting the invention into practice. The program may be in the form of source code, object code, a code intermediate source and object code such as partially compiled form, or in any other form suitable for use in the implementation of the method according to the invention. The carrier may be any entity or device capable of carrying the program. For example, the carrier may include a storage medium, such as a ROM, for example a CD ROM or a semiconductor ROM, or a magnetic recording medium, for example a floppy disc or hard disk. Further the carrier may be a transmissible carrier such as an electrical or optical signal, which may be conveyed via electrical or optical cable or by radio or other means. When the program is embodied in such a signal, the carrier may be constituted by such cable or other device or means. Alternatively, the carrier may be an integrated circuit in which the program is embedded, the integrated circuit being adapted for performing, or for use in the performance of, the relevant method.

It should be noted that the above-mentioned embodiments illustrate rather than limit the invention, and that those skilled in the art will be able to design many alternative embodiments without departing from the scope of the appended claims. In the claims, any reference signs placed between parentheses shall not be construed as limiting the claim. Use of the verb "comprise" and its conjugations does not exclude the presence of elements or steps other than those stated in a claim. The article "a" or "an" preceding an element does not exclude the presence of a plurality of such elements. The invention may be implemented by means of hardware comprising several distinct elements, and by means of a suitably programmed computer. In the device claim enumerating several means, several of these means may be embodied by one and the same item of hardware. The mere fact that certain measures are recited in mutually different dependent claims does not indicate that a combination of these measures cannot be used to advantage.

Claims

CLAIMS:

1. A system for computing a projection image from a volume data set, in particular a medical imaging volume data set, comprising: means (702) for determining a plurality of rays intersecting the volume, each ray being associated with a respective pixel in the projection image; means (704) for collecting a plurality of intensity values associated with voxels in a neighborhood of a ray of the plurality of rays; means (706) for associating each respective weight of a plurality of predefined weights with a respective intensity value of the plurality of intensity values in dependence on an ordering of the plurality of intensity values with respect to intensity, at least two weights of the plurality of weights being nonzero and at least two weights of the plurality of weights having a mutually different value; means (708) for computing a weighted sum of the intensity values using the associated weights; and means (710) for associating an outcome of the weighted sum with the respective pixel.

2. The system according to claim 1, wherein for any two intensity values of the plurality of intensity values where a first intensity value is smaller than a second intensity value, it holds that a weight associated with the first intensity value is smaller than or equal to a weight associated with the second intensity value.

3. The system according to claim 1, wherein for any two intensity values of the plurality of intensity values where a first intensity value is smaller than a second intensity value, it holds that a weight associated with the first intensity value is greater than or equal to a weight associated with the second intensity value.

4. The system according to claim 2 or 3, wherein the plurality of weights comprises a first sequence of linearly increasing weights and a disjunct second sequence of linearly increasing weights, where the first sequence increases with a different value than the second sequence.

5. The system according to claim 1, comprising means for sorting the plurality of intensity values according to the ordering to form a sorted list; and wherein the means for associating the weights is arranged for performing the associating based on a position of each intensity value in the sorted list.

6. The system according to claim 0, wherein a difference between any two weights associated with two successive intensity values in the list is fixed.

7. The system according to claim 0, wherein a difference between any two weights associated with two successive intensity values in a first portion of the list is equal to a first fixed value, and a difference between any two weights associated with two successive intensity values in a second portion of the list is equal to a second fixed value, the portions of the list being disjunct and both portions of the list consisting of a series of subsequent positions in the list.

8. A method of computing a projection image from a volume data set, in particular a medical imaging volume data set, comprising determining (502) a plurality of rays intersecting the volume, each ray being associated with a respective pixel in the projection image, and for individual rays (504) collecting (506) a plurality of intensity values associated with voxels in a neighborhood of the ray; associating (508) each respective weight of a plurality of predefined weights with a respective intensity value of the plurality of intensity values in dependence on an ordering of the plurality of intensity values with respect to intensity, at least two weights of the plurality of weights being nonzero and at least two weights of the plurality of weights having a mutually different value; computing (510) a weighted sum of the intensity values using the associated weights; and associating (512) an outcome of the weighted sum with the respective pixel.

9. A computer program product comprising instructions for causing a processor to perform the method according to claim 8.