AEDL Algorithm for Change Detection in Medical Images - An Application of Adaptive Dictionary Learning Techniques

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1 AEDL Algorithm for Change Detection in Medical Images - An Application of Adaptive Dictionary Learning Techniques Varvara Nika 1, Paul Babyn 2, and Hongmei Zhu 1 1 York University, Department of Mathematics & Statistics, nikav@mathstat.yorku.ca, hmzh@mathstat.yorku.ca 2 University of Saskatchewan, Department of Medical Imaging, paul.babyn@saskatoonhealthregion.ca Abstract. Change detection algorithms aim to identify regions of changes in multiple images of the same anatomical location taken at different times. The ability to identify the changes efficiently and automatically is a powerful tool in medical diagnosis and treatment. Although many have investigated ways of automatic change detection algorithms, challenges still remain. The key of detecting changes in medical images is to detect disease-related changes while rejecting unimportant ones induced by noise, mis-alignment, and other common acquisition-related artifacts (such as intensity, inhomogeneity). In this paper, we propose a new approach for detecting local changes based on adaptive dictionary learning techniques. The proposed AEDL, Adaptive EigenBlock Dictionary Learning, algorithm captures local spatial difference between the reference and test images via detecting the significant changes between the test and the reference image linearly modeled by a local dictionary trained from the reference and the test images and reconstructed by local sparse minimization processes. The AEDL algorithm is designed to ignore insignificant changes due to mis-alignment (such as spatial shift, rotation), field inhomogeneity, and noise. To reduce the size of local dictionaries in the algorithm and to identify the linear relationship in the data, the principle component analysis is employed, which helps to speed up the computation for practical applications. Performance of our algorithm is validated using synthetic and real images. Keywords: Computer-aided diagnosis, dictionary learning, change detection, principal component analyis. 1 Introduction Change detection algorithms intend to identify regions of changes in multiple images of the same scene taken at different times. [2 4] have shown that automated change detection systems can reduce human error and minimize the enormous amount of data that radiologists have to process to reach a conclusion. A good survey on the change detection algorithms can be found in [4]. [2] presents an automatic change detection system for serial MRI with applications in multiple sclerosis follow-up. Their method based on integrating generalized likelihood ratio test and nonlinear joint histogram normalization often fails when noise is non-stationary. Patriarche and Erickson implemented an integrated system for detecting changes in serial multi-spectral MRI examination [3, 7 9]. Their algorithm is based on post classification of image pixels in multi-spectral MR intensity feature space, with the assumptions that an abnormal tissue may look like a tissue transitioning from one normal tissue to another in the feature space and that change tends to occur along lines connecting pairs of cluster centroids in the feature space. Preliminary clinical studies show that their system can identify visually subtle changes related to disease. However, tissue classification task itself is very difficult; in addition, the whole process of calculating transition tissue types and fractional membership for each pixel is inherently time-consuming. A general nonparametric statistical framework and a cosine similarity measure were introduced in [11] to detect changes in two MR images from a single MRI modality. However, the effect of mis-alignment was not addressed in that work. Background modeling [10] offers another main approach for change detection problems. Changes can be revealed by subtracting the background from the test image. Most images are sparse in either spatial domain or some transformed domain. In particular, changes in an image, i.e., the background subtracted image, is generally sparse spatially. With fast development of compressive sensing (CS) [5, 6] and availability of various sparse image reconstruction algorithms, it s natural to explore the use of CS in change detection, such as in [10, 15]. Any application of CS to background subtraction models involves the use of various L1 minimization algorithms. Recently, many MRI reconstruction techniques employ compressive sensing methods. Lustig s work is very well known among others for a direct application to MR images of the brain, etc. [18] uses a well known fact, that MR images are sparse in some domains, such as wavelet, finite differences, etc. He recovers an undersampled MR image by using L1 minimization,

2 2 AEDL Algorithm for Detecting Changes in Medical Imaging which allows for rapid MR imaging. One of the major challenges in change detection algorithms for medical images is to detect diseaserelated changes while rejecting changes caused by noise and acquisition-related artifacts, such as misalignment and intensity inhomogeneity. Despite the diversity of approaches [2 4, 7 11], a change detection algorithm usually consists of many common pre-processing steps to suppress or filter out unimportant changes before making change detection decisions and using the core algorithm to determine the set of pixels that are significantly different from the reference image and are disease-related. The sequence of pre-processing steps complicate the algorithm as a whole, increase the processing time, and most importantly may distort clinical relevant information in the original images. [15] addresses mis-alignment and change detection problem together by employing a series of sparse optimization problems. However, their method only works well for highly sparse images, such as SAR images that are much sparser than most medical images. Hence, this motivates us to develop an algorithm that can automatically tolerate noise and acquisition-related artifacts but captures subtle and important clinical changes in medical images that are not highly sparse spatially. In this paper, we propose a method for detecting local changes in medical images based on adaptive dictionary learning techniques. To simplify the problem, we focus on detecting differences between two images, namely, reference and test images. Note that these two images are not necessarily aligned and may contain different noise level, intensity inhomogeneity, and other acquisitions related artifacts. Roughly speaking, the proposed Adaptive Eigenblock Dictionary Learning (AEDL) algorithm consists of three stages: 1) Captures local spatial changes between the reference and test images by averaging all the absolute differences of a test image block with its best linear approximations given by a local dictionary trained from the reference image. As a sparse linear combination of the image blocks in the dictionary, the modeled background image can be reconstructed by the L1-minimization algorithm. 2) Repeat stage one by averaging all the absolute differences of a reference image block with its best linear approximations given by a local dictionary trained from the test image. 3) Finally, the changed detection image is the average of changed detection images from stages one and two. Our approach not only extends previous work [1, 13 16], but also introduces the use of PCA to reduce the size of a local dictionary for each image block and hence improve computational efficiency. 2 Adaptive EigenBlock Dictionary Learning Algorithm Let I 1 and I 2 represent two images of size N N taken at two different times, respectively. I s(i,j) is image intensity of the pixel at row i and column j for s= 1 or 2. Let a ij and b ij be blocks of size(2δ +1) (2δ+1) in the reference and test images centered at pixel I s(i,j), where parameter δ is the radius of blocks a ij and b ij. Stacking columns of a ij and b ij form a column vector x ij and y ij of size M 1, where M=(2δ +1) 2 and δ is a positive integer. Fig. 1. a) Reference and b) test images; c) b ij block from the test image of size 3 3 and centered at 64th row and 64th column; d) the corresponding B ij block from reference image of size 5 5 (δ=1, c=1); e) dictionary Φ ij of size 9 25 (25 blocks of size 3 3) We assume that two images differ from one another from disease related changes that have occurred from time t 1 to time t 2, and also from registration shifts, rotations, etc. During this time interval each block from the reference image has undergone through few disease related changes. Most pixels of the

3 AEDL Algorithm for Detecting Changes in Medical Imaging 3 reference image will appear again in the test image either at the same location or nearby. This means that each block b ij from the test image, can be sparsely represented as a linear combination of few blocks a ij from the reference image, over a dictionary Φ ij. Our algorithm seeks to automatically find the linear relationship in the data. Fig 1 shows an example of how dictionary Φ ij is created. Most existing methods, such as those in image surveillance and face recognition [1, 13 16], learn the dictionary using training samples from a database of images. In our method during stage one we use the reference image to learn the dictionary. We propose a block based dictionary which will capture only local disease related changes and will ignore the changes due to the patient positioning, etc. We use overlapping blocks to reduce image block artifacts. Fig 2 shows an example of a b ij block from a test image of size 3 3, the corresponding B ij block from the ref image of size 9 9. (δ=1, c=3), and dictionary Φ ij of size 9 81 (81 blocks of size 3 3). Columns of the dictionary are obtained by projecting blocks from reference image onto the Eigen subspace. In our algorithm, for each block b ij in the test image, we consider a block B ij in the reference image I 1 of size (2 +1) (2 +1) centered at a pixel I 1(i,j), as Fig 1 and Fig 2 show, where = δ+c, with c=1,2,3... Our method seeks to represents a vector y ij from test image as a sparse linear combination of vectors x ij from the reference image over a dictionary Φ ij. Fig. 2. (Left) shows a B ij block (orange color) of size 9 9, from reference image I 1, with many overlapping a ij blocks (light green color) and of size 3 3. Here δ=1, c=3, and = δ+c=4. (Right) shows an example of b ij of size 3 3 from the test image I 2, and centered at ith row and jth column. In this case, dictionary Φ ij is of size 9 81 y ij = Φ ij γ ij (1) where γ ij is a sparse vector with only few nonzero elements. We try to find the sparsest vector γ ij that satisfies Eq. (1), by solving the following minimization problem: ˆγ ij = argmin γ ij 0 s.t. y ij = Φ ij γ ij (2) To account for noise, Eq. (1) can be modified as: y ij = Φ ij γ ij + r ij (3) where r ij = y ij Φ ij γ ij are the residual errors in approximation algorithm. It is clear that our task is now to minimize r ij. L 0 minimization problem(2) can be relaxed into a L 1 convex minimization problem given as: ˆγ ij = argmin γ ij 1 s.t. y ij = Φ ij γ ij + r ij (4) Eq. (3) can be rewritten : y ij = [Φ ij I][γ ij r ij ] T A ij α ij (5)

4 4 AEDL Algorithm for Detecting Changes in Medical Imaging For every vector y ij from the test image, we want to determine the sparsest representation ˆα ij of α ij, which minimizes the error r ij, so that (5) is true. Equivalently, solve the following minimization problem. ˆα ij = argmin α ij 1 s.t. y ij = A ij α ij where: α ij = [γ ij r ij ] T and ˆα ij = [ˆγ ij ˆr ij )] T (6) To reduce the noise, A ij can be modified slightly by spreading out the mean value µ of B ij. A ij = [Φ ij µi] (7) Here I is the identity M M matrix. An orthogonal matching pursuit algorithm can be used to solve (6). In our experiments we use CoSaMP [12] to compute ˆα ij by minimizing the L 1 norm. The best approximation ŷ ij of the block y ij from the test image is then calculated as: ŷ ij = Φ ij ˆγ ij and r ij = ŷ ij y ij (8) 3 Dictionary Learning via Projection onto Eigen-Subspace In Eq. (7), dictionary Φ ij of size M P where P=(2 +1) 2 composed from reference image atoms, posses high level of redundancy. This is because many pixels are included in more than one atom. We thus use PCA to reduce the dimensionality of the dictionary dataset and eliminate such redundancy. The general idea is to approximate each column x ij of Φ ij, with ˆx ij of ˆΦ ij, such that: ˆΦ ij = T Φ ij (9) where T is a M M transform of rank r<m. The best choice for the transform T would be the one that minimizes the residual error, the MSE (mean square error). This transform is: T = r V s V T s (10) s=1 T is the orthogonal projection onto the space spanned by V 1, V 2,..., V r eigenvectors of covariance matrix of Φ ij. Blocks a kl from B ij, with k = i,..., i + and l = j,..., j +, are stacked as column vectors x kl of size M 1 and make up the columns of Φ ij. Φ ij = [x i,j,..., x ij,..., x i+,j+ ] (11) Columns x c kl of dictionary Φc ij, are computed by subtracting the average of Φ ij. Eigenvalues and Eigenvectors of the covariance matrix Ω = Φ c ij (Φc ij )T are then computed. The projection Φ ij of the dictionary Φ c ij onto Eigen-Subspace of Ω is computed as: A low dimensional dictionary is then computed as: Φ ij = V T Φ c ij (12) ˆΦ ij = V r Φ ij (13) where V r is the matrix of r eigenvectors corresponding to r largest Eigenvalues. Equation (7) can be written as: And our initial problem (6) will be written as: Â ij = [ ˆΦ ij µi] (14) ˆα ij = argmin α ij 1 s.t. y ij = Â ij α ij where: α ij = [γ ij r ij ] T and ˆα ij = [ˆγ ij ˆr ij ] T (15) Sparse approximation of column vector y ij, and the residual error of the approximation are then calculated as:

5 AEDL Algorithm for Detecting Changes in Medical Imaging 5 ŷ ij = ˆΦ ij ˆγ ij (16) where: r ij = ŷ ij y ij (17) The changed detected image, CD xy is created by placing residual vectors r ij as blocks of size M = (2δ +1) (2δ+1), centered at the pixel (i,j), and divided by n, where n is the number of b ij blocks that contain that pixel. In stage two, the process is repeated by switching the reference image with the test image and computing CD yx. Then in stage three, the two changed detection images, CD xy and CD yx are averaged to create the final change detected image CD. 4 Experiments We tested our method first by using synthetic images of size , shown in Fig.3 to Fig.6. There are three 12 sided polygons placed in the first 32 rows of the reference image. The size of each polygon increases from left to right and pixels inside each polygon were given intensities using Gaussian distribution with maximum intensity 0.3, 0.2, 0.4 respectively, from left to right. To test the algorithm for different shifts sizes, rotation angles, noise and intensity levels, we applied similar constructions for rows 33 to 128. This means that we place the same three polygons to the second, third, and fourth 32 rows of the reference image. The test image is created by making two types of changes to the reference image, significant and insignificant changes. Changes such as shifts, rotations, and different noise levels, added to different strips of the reference image, are called insignificant changes. In addition to insignificant changes, the reference image has gone under other changes, considered significant, such as: the second shape in the second 32 rows is deleted, a new shape is added (down-right), the shape in the fourth 32 rows and first 32 columns is enlarged, and finally, the third polygon of the second 32 rows is decreased. These significant changes make up our ground truth image. The desired outcomes of a change detection algorithm is to detect only the significant changes that make up the ground truth image. The performance of the AEDL is compared with the ground truth and the absolute difference method. In Fig.3, strips of 32 rows of reference image are shifted 1-down and 1-left, 3-down and 2-right, 2- down and 3-left, and 3-up and 4-right, respectively, which are considered insignificant changes. AEDL algorithm ignores the changes related to horizontal and vertical translations of images strips when the radius of B ij is greater or equal to the size of the shift, but detects the real and significant changes closer to the ground truth, with δ =1 and c=3 than the absolute difference. In Fig.4, strips of 32 rows of reference image are rotated by 2 degrees clockwise,3 degrees counter-clockwise, 4 degrees clockwise, and the last 32 rows by 6 degrees counter-clockwise, which are considered insignificant changes. Results show, again, that the AEDL algorithm ignores the changes related to rotation of strips when the radius of B ij to the angle of rotation and detects the significant changes closer to the ground truth with δ=2 and c=3. In Fig.5, Gaussian noise is added to the reference image, with SNR = 30, 40, 50, and 60 for the first, second, third, and fourth 32 rows respectively, which are considered insignificant changes. The simulations show that the AEDL algorithm still detects the real changes closer to the ground truth for SNR 30 with δ=1 and c=3. In Fig.6, starting from the second strip of 32 rows in the reference image, the intensities of shapes on the second, third, and fourth strips are increased by 0.1, 0.3, and 0.5 respectively. We want our algorithm to detect changes due to the intensity changes, as they are considered disease related by the radiologists. Shapes at the bottom of the test image have a maximum intensity of 0.9. Therefore, we added these changes to our previous ground truth image which now serves as the ground truth for this experiment. AEDL algorithm still detects the significant changes closer to the ground truth, with δ=1 and c=1. In Fig.7, we also tested AEDL algorithm with MR images. Row a) shows the results of two real T2 weighted MR images taken in 2010 and Both images have the same inactive and visible MS lesion, which hasn t grown or changed between two exams periods, as confirmed by the radiologist. The fifth image, a superposition of the test image with the colored changed image, is the same as the test image, showing that there were no significant changes for the algorithm to detect, and the absolute difference shows changes due to the image registration which are considered as insignificant by our algorithm and therefore ignored. Row b) shows two T2 weighted MR images, with 1mm slice thickness, 3% noise, and 0% intensity non-uniformity (RF). Images are obtained from brainweb: simulated brain database [17]. AEDL algorithm finds the significant changes related to the new MS lesion formation and ignores changes shown from the absolute difference.

6 6 AEDL Algorithm for Detecting Changes in Medical Imaging 5 Conclusions and Future Work In this paper we presented an application of adaptive dictionary learning techniques with a new change detection algorithm AEDL. The algorithm captures local spatial changes between the reference and test images and consists of three stages. In the first stage, changed detection image is obtained by averaging all the absolute differences of a test image block with its best linear approximations given by a local dictionary trained from the reference image. In stage two the process is similar, but the local dictionaries are learned from the test image blocks. In the third stage, the changed detection image between the reference and test image is computed as the average of changed detection images from stages one and two. The sparse approximation can be computed by the L 1 - minimization algorithm. This algorithm automatically detects the significant structural changes in the test image while ignoring unimportant changes related to mis-alignments, noise and acquisition-related artifacts. Experiments on synthetic images illustrated that our algorithm detects changes due to appearance or disappearance of objects in the presence of object translations, rotations, intensity changes, and moderate noise level. Experiments on MR images showed that our algorithm identifies clinically significant changes and rejects clinically insignificant changes. Note that the rejection of unimportant changes has to be within areas of local dictionaries. In addition, we introduced the use of PCA to reduce the size of a local dictionary for each image block, to find the linear relationship in the data, and improve computational efficiency. This paper shows our preliminary results. More clinical data will be collected to validate the algorithm. Further investigation is needed to improve the performance to account for high noise level and accuracy. 6 Simulations Fig. 3. Testing the algorithm performance in the presence of object shifts. a) Reference image. b) Test image c) Ground truth image showing only the significant changes. d) Absolute difference image between the test and reference images. e) Changed detection image by AEDL approach shows that the algorithm ignores the changes related to translations that can be captured by local dictionaries, but detects the real and significant changes closer to the ground truth. Fig. 4. Testing algorithm performance in the presence of object rotations. a) Reference image. b) Test image c) Ground truth image showing only the significant changes. d) Absolute difference image between the test and reference images. e) Changed detection image obtained by AEDL algorithm shows that our method ignores the changes related to rotations that can be captured by local dictionaries, but detects the significant changes closer to the ground truth.

7 AEDL Algorithm for Detecting Changes in Medical Imaging 7 Fig. 5. Testing algorithm performance in the presence of different noise level. a) Reference image. b) Test image c) Ground truth image showing only the significant changes. d) Absolute difference image between the test and reference images. e) Changed detection image obtained byaedl is very closer to the ground truth and shows that our algorithm method detects the real changes for SNR ratio > 25. Fig. 6. Testing algorithm performance in the presence of different intensity level. a) Reference image. b) Test image c) Ground truth image showing only the significant changes. d) Absolute difference image between the test and reference images. e) shows that the changed detection image obtained by AEDL algorithm detects the significant changes closes to the ground truth image. Fig. 7. a) From left to right, the reference and test images of the same patient taken at two year interval identified with no significant disease related changes, changed image given by AEDL method showing no significant changes, absolute difference image between reference and test images showing changes due to mis-registration, the test image overlaid with the coloured changed image;( b) Results for two T2-weighted MR images of a normal brain and a brain with moderate MS lesions simulated by BrainWeb [17]. AEDL algorithm detects the significant changes related to the MS lesions and ignores unimportant changes which the absolute difference image shows.

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