AUTOMATED DETECTION OF BLOB STRUCTURES BY HESSIAN ANALYSIS AND OBJECT SCALE

Jiamin Liu, Jacob M. White, Ronald M. Summers

Imaging Biomarkers and Computer-Aided Diagnosis Laboratory

Department of Radiology and Imaging Sciences National Institutes of Health Clinical Center

Building 10 Room 1C368X MSC 1182 Bethesda, MD 20892-1182

ABSTRACT Automated detection of blob-like structures is desirable in many biomedical applications such as nodule detection in radiographs and CT images, lymph nodes detection in CT images, and cell counting or tracking in biological images. Multiscale analysis of Hessian matrix is widely used for enhancement or detection of blob-like structures in two-dimensional (2D) and three-dimensional (3D) images. We proposed a new blob detector and a new detection response measure, blobness, based on eigenvalues of the Hessian matrix and local object scale. Pixels with higher blobness are clustered as detected blobs. We evaluated our method by comparison with two existing methods on both simulated and real images. Our results indicated that our automated blob detector had better performance on those images especially when the blobs were close to each other. Our method can be easily extended to 3D for computer-aided detection of blob-like structures in medical images.

Index Terms—blob detection, Hessian matrix, object scale.

1. INTRODUCTION Automated detection of blob-like structures is desirable in many applications. Examples include, lung nodule detection in chest radiographs [1] and thoracic CT scans [2], lymph node detection in chest/abdominal CT images, and cell counting or tracking in biological images [3]. The localization and distribution of these blob-like structures are required for further analysis in these applications.

Multiscale analysis of the Hessian matrix, i.e. second derivatives in orthogonal directions at each location, is widely used for enhancement or detection of line-like structures in two-dimensional (2D) and three-dimensional (3D) images. Based on the eigenvalues of the Hessian matrix, a local pattern is classified as plate-like, line-like or

blob-like structures. The method was originated by Koller et al. [4] and was further developed by Lorenz et al. [5] and Frangi et al. [6] for the purpose of vessel enhancement. Sato et al. [7] also developed a line enhancement filter based on the eigenvalues of the Hessian matrix, and generalized their filter for blob enhancement. One known problem of this kind of method is too much blurring can occur during the multiscale smoothing lead to false detections, especially for close-by structures.

In this paper, we propose a new blob detector and a new detection response measure, blobness, based on Hessian analysis and a local object scale [8, 9]. Pixels with higher blobness are clustered as detected blobs. Object scale proposed by Saha al. etc. [8, 9] is a fundamental, well-established concept in image processing. This concept has been successfully used in segmentation [8], filtering [9], and registration [10]. The premise behind the concept of scale is to consider the local size of the object in carrying out whatever local operations are done on the image. Since this local size is determined at every image pixel and represents the geometric information of those blob-like structures, it makes sense to consider local object scale in the blob detection response measure.

The complete methodology of our approach is described in Section 2. We demonstrate the results in Section 3. Our concluding remarks are stated in Section 4.

2. METHODS

In this section, a new detection response measure, blobness, is defined based on eigenvalues of the Hessian matrix and the object scale at every pixel in the image. Pixels with higher blobness will be clustered as detected blobs. The method consists of two stages: object scale computation and multiscale Hessian analysis.

2.1. Object scale computation

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Proceedings of 2010 IEEE 17th International Conference on Image Processing September 26-29, 2010, Hong Kong

First a local object scale [8] is computed at every pixel in the image. The object scale k at every pixel is defined as the radius of the largest hyperball centered at the pixel such that all pixels within the ball satisfied a predefined image intensity homogeneity criterion. Under this definition, object scale represents the geometric information (size) of local structure. Object scale at the center of a blob-like structure approximately equals the radius of the blob in pixel size. Object scale at the boundary usually is very low (0 or 1 pixel). This information is very useful during the design of the detection response measure in the next step.

2.2. Multiscale Hessian analysis

We computed the Hessian matrix for each pixel in the image by convolution with the second and cross derivatives of a Gaussian with scale :

yyyx

xyxx

II

IIH =

σ (1)

I(x,y) is the image intensity at pixel (x,y). Its corresponding eigenvalues are 1 and 2 (| 2| | 1|). For each voxel, we defined a blobness B ( ), detection response measure as:

=<=

−

otherwise0

2,1for0if)(

2

1

2 2

ieB i

/Rc λλ

λ

λσ

(2)

with σ2−= kRc (3)

The detection response B ( ) will be maximum when , k, and the actual size (radius) of the blob to be detected approximately match (i.e. 2× = k = radius of detected blob in pixel size). Ideally, the center of the blob has the maximal detection response. The in B indicates that blobness is computed on a smoothed version of the original image and is therefore representative of the variations of image intensity at the spatial scale .

Finally the maximum response B ( ) is selected for every pixel:

)(max)(],[ maxmin

λλσ

σσσ

BB∈

= (4)

The pixels with higher blobness are labeled as detected blobs.

3. RESULTS

In this section, the performance of our blob detection was evaluated with both simulated and real images.

3.1 Results on simulated images

In order to understand how the detector filters perform on the idealized shapes, we applied the blob detection on idealized blobs in 2D images.

Figure 1(a) shows a simulated image with five idealized blobs and three lines. The radius of five blobs (from left to right) is 4, 4, 6, 10, 12 pixels, respectively. The width of three lines (from top to bottom) is 2, 4, 6 pixels, respectively. Gaussian smoothing with =3 was applied to blur the image. Two dots with a radius of 4 pixels are located very closely to make the detection more challenging.

First, we attempt to compare our detection with two existing enhancement filters [6, 11] because these filters employed the eigenvalues of the Hessian matrix as well. The difference between those methods is how to define the blobness. Frangi et al. [6] proposed the blobness based on all eigenvalues, in both of which three unknown parameters must be determined empirically. Li et al. [11] further simplified their blobness defination without any parameters.

Figure 1(b), (c) and (d) show the detected blobs overlaid on the original image (Figure 1(a)) by applying Frangi’s method, Li’s method, and our blob detector, respectively. We employed five smoothing scales of 4, 6, 8, 10 and 12 pixels for all three methods. It is apparent that all three methods successfully detected the isolated blobs without detecting line-like structures. However, if two blobs are very close to each other, the two existing methods can not distinguish them and detect them as one big blob (Figure 1(b) and (c)). This is because the high smoothing factor ( =12) in the multiscale Hessian analysis caused strong detection response in the close-by boundary regions of two dots. The new blobness proposed in this paper had an extra

term 22 /Rce− which had weak detection response in boundary regions and thus distinguished and detected the two close-by blobs (Figure 1(d)).

It should also be noted that all three blob detection filters responded to the outer regions of lines because these regions appear like blobs locally. These false detections can be easily removed by other features such as volume.

3.2. Results on real images

We also compared the three detection methods using a real image (Figure 2(a)). Figure 2(b), (c) and (d) shows the detected blobs by applying Frangi’s method, Li’s method, and our method, respectively. Four smoothing scales of 4, 6, 8 and 10 pixels were utilized in all three methods. It is apparent that the isolated blobs on the butterfly were successfully detected by all three methods. However, for the blobs that are very close to each other (shown in the red circled regions in Figure 2(a)), the two existing methods can not distinguish them and instead detected them as a big blob (Figure 2(b) and (c)). Our method correctly detected them as individual blobs (Figure 2(d)).

842

(a) (b)

(c) (d) Figure 1. Comparison of simulated images with five idealized dots (from left, radius=4, 4, 6, 10, 12 pixels) and three idealized lines (from top, width=2, 4, 6 pixels). (a) Original image, (b) detected blob image overlaid on the original image with Frangi’s method, (c) detected blob image overlaid on the original image with Li’s

method, and (d) detected blob image overlaid on the original image with our method.

(a)

(b)

(c)

(d)

Figure 2. Comparison of real images. (a) Original image (http://wwwx.cs.unc.edu/~sjguy/CompVis/Features/), (b) detected blobs with Frangi’s method, (c) detected blobs with Li’s method,

and (d) detected blobs with our method.

3.3 Results of 2D CT images

In this section, we applied our blob detection method to a CT image. Figure 3(a) shows one slice of an abdominal CT scan that depicts an enlarged lymph node (greater than 1cm in diameter). Since lymph nodes are usually adjacent to blood vessels, we only applied our blob detection to those pixels within 30 pixels of particular blood vessels (red circles in Figure 3(b)). The detected lymph node (yellow) and several false positives are shown in Figure 3 (b).

4. DISCUSSION AND CONCLUSIONS

The use of eigenvalues of the Hessian matrix has been investigated by a number of researchers for the development of vessel enhancement filters. The same concept was also employed for construction of blob, line, and plate enhancement filters by Sato et al [7].

In this paper, we have proposed an automated detector of blob structures that uses both Hessian analysis and object scale. Local structure (by object scale) and shape discrimination (by Hessian analysis) are simultaneously considered into the detection response measure.

843

(a)

(b)

Figure 3. (a) Example CT slice image magnified to show region of interest. (b) Detected lymph node (yellow) and false positives (blue). Blob detection was only applied to the pixels within 30

pixels of the indicated blood vessels (red circles).

The detection task should be distinguished from the segmentation task, the latter accounting for target localization accomplished together with exact shape reconstruction. The output of detection can be used as seed points for automated segmentation of blob-like structures such as lymph nodes. Once the segmentation is automated, further analysis can be automated.

The detection of single or isolated blobs is not difficult. Detection is more complicated when blobs and other structures are very close to each other, which is normal in real images, especially in biomedical images. This is because the smoothing during the multiscale Hessian analysis blurs the boundaries too much and thus causes a strong detection response in the close-by boundary regions. The new method proposed in this paper overcame this

problem by introducing an object scale-based term 22 /Rce− in the blobness definition. This term produces a weak detection response in those regions and diminishes this problem.

Hessian analysis and object scale computation for 3D images are straightforward; therefore the blob detection described in this paper can be easily extended to 3D for medical applications, such as computer-aided detection of lung nodules or lymph nodes in CT images. In these applications, some known anatomic properties, including intensity, volume, and shape, should be used to reduce false-positives from the detected blob-like candidates.

Finally, we conclude that the new blob detector has potential application in computer-aided detection of blob-like structures in medical images.

5. ACKNOWLEDGMENT This research was supported by the Intramural Research Program of the NIH Clinical Center.

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