Abstract: In this paper, a novel automated and precise detection of brain tumor technique is presented. The brain tumor in an MR slice is detected by an axis-parallel box that circumscribes the entire tumor, more precisely. This work is carried in two phases. First is Crude detection phase, which detects the sub-region that contains the major portion of the tumor. This phase searches for the most dissimilar sub-region between the left and the right halves of a brain in MR slice. In our approach, dissimilarity detection is based on Bhattacharya coefficient computed with gray level intensity histograms, Standard deviation, and Mean intensity distances. . But this detected sub-region may not cover the tumor entirely and precisely. Hence in the second phase, the precise locating of the four edges of the crudely detected sub-region, by searching their accurate locations is dealt. The minima in the Bhattacharya Coefficient ‘ plots or the maxima in the Standard Deviation or Mean Intensity distance – plots, dictate the accurate locations of the edges. These edges are used to form the axis-parallel box that is overlaid on the tumor in MR slice. Experimental results show that, our detection method, is more precise compared to other histogram-based bounding box techniques.

Keywords: Brain tumor, MRI, Precise detection, Bounding box, Bhattacharya Coefficient, Standard Deviation, Mean Intensity.

1. Introduction

According to a statistical survey, tumors are the second cause of cancer-related deaths in children under the age of 20, in adults of age 20 to 39 [1-5, 8]. This enhanced the growth in researches on the tumor detection and helped the doctors to rescue lives by detecting the disease earlier and initiates necessary treatment. Currently, radiologists locate the tumors in MR images by hand; this manual detection process is tedious and time-consuming. Also, it requires prior domain knowledge and experience on radiology for accurate tumor detection in medical imaging. Automation of tumor detection is required, as there is a shortage of skilled radiologists at a time of great need.

Varieties of image processing techniques are available for tumor detection that will detect certain features of the tumors such as the shape, border, calcification, and texture. These features will make the detection processes more accurate and easier, as there are some standard characteristics of each feature for a specific tumor [6-7].

The paper is organized in the following sections: Survey of the related work is carried in the section 2. Concepts of dissimilarity detection using Bhattacharya Coefficient are explained in the section 3. In section 4 we discuss our proposed technique which consists of Crude detection and Precise detection phases, with the experimental results and discussions. We deal with the conclusion of the paper in section 5.

2. Literature survey

The detection of medical images is a challenging task due to the complexity of tumor characteristics in images, such as sizes, shapes, locations, intensities and large variance of tumors. Statistical classification based on pixel using multipara-meter images are most common [9], [10]. But they fail to consider global shape and boundary information. Classifica-tion approaches for brain tumor segmentation have met with only limited success due to overlapping intensity distribu-tions of healthy tissue, tumor, and surrounding edema [11], [12]. Assuming that lesion pixels are distinctly different from normal tissue characteristics, lesions or tumors were considered as outliers of a mixture Gaussian model for the global intensity distribution, [13], [14]. Many attempts used elastically fitting boundaries [15], interactive segmentation tools [16]. Methods based on mathematical morphology [17], neural networks [18], texture differences between normal and pathological tissue [19]. A geometric prior can be used by atlas-based segmentation, which detects abnormal regions by considering a registered brain atlas as a reference for healthy brains. But to accommodate the tumors, these techniques need to significantly modify the brain atlas which leads to poor results. High-dimensional warping methods require elastic registration of images to account for geometrical distortions produced by pathological processes. Such registration is challenging and is not yet solved for the general case. Elastic atlas registration with statistical classification is combined by Warfield et al. [20], [21]. To improve separation of clusters in multi-dimensional feature space, it uses ‘distance from brain boundary’ as an additional feature. A supervised selection of training regions is required for the initialization of probability density functions. In this paper, the new method is presented to combine statistical classification with spatial information to consider the overlap of distributions in intensity feature space. Automatic segmentation of MR images of normal brains, using an atlas prior for initialization and also for geometric constraints by statistical classification was de-veloped by Leemput et al. [22], [23].

A bounding box technique, by comparing the left-right symmetry of the brain is developed as in Nilanjan Ray’s algorithm [24]. Here vertical sweep and a horizontal sweep of the axial MR slice produce score plots. The maxima and the minima from the plot using vertical sweep are detected as top and bottom edges and from the plot using horizontal sweep are detected as left and right edges of the bounding box. And the corresponding bounding box is overlaid on the input MR image that detects the tumor. But the bounding box with this technique fails to circumscribe the tumor entirely and exactly.

3. Dissimilarity detection

We present an automatic precise detection technique that avoids the above problems, by locating a ‘bounding box’ ‘ i. e., an axis-parallel rectangle, exactly around the entire tumor on an MRI slice. This bounding box can then be used to derive the useful data about the tumor, viz., position, size, growth rate etc.

On each input MR slice (axial view), the algorithm first locates the left-right axis of symmetry of the brain [24], which divides the brain into 2 hemispheres. The left (or the right) half serves as the test image I, and the right (or the left) half supplies as the reference image R. A tumor typically perturbs this symmetry. Thus, the algorithm searches for an axis-parallel rectangle on the left side that is very dissimilar from its reflection about the axis of symmetry on the right side ‘ i.e., the intensity histograms of two rectangles are most dissimilar, but the intensity histograms of the outside of the rectangles are relatively similar. We assume that one of the two rectangles will circumscribe the tumor appearing in one hemisphere of the brain. The degree of dissimilarity between two normalized intensity histograms is quantified using Bhattacharya Coefficient.

Bhattacharya Coefficient (BC) is a measure of the correlation between two histograms. It is expressed as the inner product between square roots of two normalized histograms [25]. Let A(s) and B(s) be the portions of the image domain, s, respectively. Let BC(s) denote Bhattacharya Coefficient between them, given by equation (1):

(1)

where, denote normalized intensity histograms (probability mass functions of image intensities), the of test image within A(s) or of reference image within B(s). Bhattacharya coefficient is a real number between 0 and 1. Its value is 1 for two identical normalized histograms; whereas is 0 for the completely different histograms [25].

Further, we have attempted to measure the dissimilarity by finding the Euclidean distance between Standard Deviation (SD) of a sub-region in one hemisphere and its reflection in another hemisphere. We found the Standard Deviation of a sub-region by finding its covariance matrix. The diagonal elements of the matrix represent variance and the square root of the variance is the standard deviation. Finally, we tried to quantify the dissimilarity by finding the Euclidean distance between Mean Intensity (MI) of a sub-region in one hemisphere and its reflection in another hemisphere. It is observed that the Euclidean distance is more for dissimilar region pairs and less for similar region pairs.

4. Proposed Technique

We have used T1-C (T1 after injecting a contrast agent) MR imaging modalities from the dataset [24], as they are good at identifying for tumor regions. The input MR slice (axial view), is subdivided into 6 regions on both the sides of the axis of symmetry. Precise detection of tumor region using Bounding box is done in two phases.

‘ Crude detection phase deals with detection of sub-region consisting of the major portion of the tumor. For this, Bhattacharya Coefficients (BC), Standard Deviation distances (SD_dist and Mean Intensity distances (MI_dist) of all sub-regions with respect to their reflections in the other hemisphere of the brain is found. The sub-region with the minimum BC or maximum SD_dist or maximum MI_dist is detected as a sub-region with major tumor portion.

‘ Precise detection phase performs precise fixing of the positions of top, bottom, right and left edges of sub-region detected by Crude detection phase. To precisely fix the position of four edges of the bounding box, the position of each edge is searched from its opposite edge in the direction of the edge to be positioned, and at each search position the Bhattacharya Coefficient (BC), Standard Deviation distance (SD_dist) and Mean Intensity distance (MI_dist) of the rectangular region are found. The values of BC, SD_dist and MI_dist are plotted v/s search positions. The minima of the steeply rising curve in BC plot or maxima in SD_dist or maxima in MI_dist dictate the precise position of the search edge.

4.1. Crude Detection of Tumor Sub-Region

The brain MRI slice is divided into 6 equal sub-regions (vertically 3 and horizontally 2) on either side of the axis of symmetry as in Fig. 1(a), 2(a) and 3(a). In each input image, Bhattacharya Coefficient (BC) is found between pair of sub-regions: Region -1 and 1s (ITLL-ITRR), Region – 2 and 2s (ITLR-ITRL), Region – 3 and 3s (IMLL-IMRR), Region – 4 and 4s (IMLR-IMRL), Region – 5 and 5s (IBLL-IBRR), Region – 6 and 6s (IBLR-IBRL). Similarly, the dissimilarity between above pair of sub-regions can also be determined using Standard Deviation distance (SD_dist) or Mean intensity distance (MI_dist) between a region and its reflection about the axis of symmetry. Standard Deviation (SD) is derived from the covariance matrix of each sub-region.

In the snap shots of Matlab Command Window in Fig. 1(b), 2(b) and 3(b), the sorted Bhattacharya coefficients (B_BC) and their corresponding region pair numbers (X_BC) are shown. In all the three cases of brain tumors considered here, region pair containing tumor, X_BC = 4 is having minimum B_BC. Similarly, the sorted Standard deviation and Mean intensity distances (b_SD and b_MI) and their corresponding region pair numbers (x_SD and x_MI) are shown. In all the three cases of brain tumors considered here, x_SD = 4 and x_MI = 4 are region pairs containing tumor, which are having maximum b_SD and b_MI.

The values of BC v/s regions, SD_dist v/s regions and MI_dist v/s regions are plotted as shown in Fig. 1(d), 2(d) and 3(d). The sub-region pair with BC minima, SD_dist maxima, and MI_dist maxima is the pair containing tumor region. Further, this pair is chosen for precisely fitting the edges of rectangular regions, as explained in the phase-2.

To determine whether the left or the right half image contains the tumor, the average intensity within the bounding boxes placed on both sides is compared. The side with higher mean image intensity within the bounding box is assumed to contain the tumor. The crudely segmented tumor regions are shown in Fig. 1(c), 2(c) and 3(c), respectively for the three tumor cases considered in this paper.

Case-1

(a) MRI slice divided into sub-regions (c) Segmented tumor sub-region

(b) Snap shot of Matlab Command Window (d) Plots of BC, SD_dist and MI_dist

Fig. 1: Detection of tumor (Case-1) sub-region pair as Region 4-4s by refering BC minima; SD_dist and MI_dist maxima

Case-2

(a)MRI slice divided into sub-regions (c) Segmented tumor sub-region

(b) Snap shot of Matlab Command Window (d) Plots of BC, SD_dist and MI_dist

Fig. 2: Detection of tumor (Case-2) sub-region pair as Region 4-4s by refering BC minima ; SD_dist and MI_dist maxima

Case-3

(a) MRI slice divided into sub-regions (c) Segmented tumor sub-region

(b) Snap shot of Matlab Command Window (d) Plots of BC, SD_dist and MI_dist

Fig. 3: Detection of tumor (Case-3) sub-region pair as Region 4-4s by refering BC minima ; SD_dist and MI_dist maxima

The Bhattacharya Coefficient, Standard Deviation-distance, and Mean Intensity’distance of a sub-region in one hemis-phere with respect to their reflection in other hemisphere are tabulated in Table 1. It can be observed that the sub-region pair containing tumor portion has maximum Bhattacharya Coefficient or minimum Standard Deviation-distance or Mean Intensity’distance.

Table 1: Bhattacharya Coefficient between a subregion and its reflection about the axis of symmetry

Bhattacharya Coefficient;

Standard Deviation Distance;

And

Mean Intensity Distance

of Sub regions

Top Extremes

Region 1-1s BC_TE 0.9982 0.9976 0.9985

SD-TE 1.0981 0.4420 1.9243

MI-TE 0.4106 0.5856 1.2646

Top Mids

Region 2-2s BC_TM

0.9972 0.9981

0.9990

SD-Tm 1.0711. 0.0548 0.3595

MI-TM 3.0248 0.9275 0.0048

Middle Extremes

Region 3-3s BC_ME

0.9937 0.9941

0.9950

SD-ME 1.1905 1.1755 0.7157

MI-ME 0.8253 2.8032 1.6019

Middle Mids

Region 4-4s BC_MM

0.9079 (BC_MIN) 0.9181 (BC_MIN)

0.9143 ( BC_MIN)

SD_MM

5.8255 (SD-dist??_MAX) 2.8953 ( SD-dist??_MAX) 9.3928 ( SD-dist??_MAX)

MI_MM

7.4900 (MI-dist??_MAX) 11.9293 (MI-dist??_MAX) 12.7132 (MI-dist??_MAX)

Bottom Extremes

Region 5-5s BC_BE

0.9965 0.9984

0.9973

SD_BE

0.7332 1.8292 0.0817

MI_BE

1.2355 2.1260 0.4433

Bottom Mids

Region 6-6s BC_BM

0.9959 0.9872 0.9725

SD_BM

0.3346 0.0844 0.6219

MI_BM

1.2139 3.5446 9.0524

4.2. Precise Detection of Tumor Sub-Region

The output of Crude Detection phase, i.e. detected pair of sub-regions, containing major tumor portion, is considered as the input in this phase. Here the top, bottom, right and left edges of the bounding box are precisely fitted to cover entire tumor accurately. The locations of the four edges of the bounding box are fitted by the following the procedure below.

Fitting of Top edge: The Precise location of the top edge of crudely detected sub-region is searched from the bottom edge of the sub-region in vertical upward direction. Bhattacharya Coefficient at each search location is noted down. The minimal point (x = 41 pixels) of the steepest rising curve of the plot of Bhattacharya Coefficients v/s search location in pixels is the location of top edge of the rectangular sub- region, as shown in Fig. 4(c) ‘ (i).The segmented region with the top edge precisely fitted is shown in the Fig. 4(b) ‘(i).

Fitting of Bottom edge: The Precise location of bottom edge of the rectangular sub- region is searched from fitted top edge of the sub-region in vertical downward direction. Bhattacharya Coefficient at each search location is noted down. The minimal point(x = 67 pixels) of the steepest rising curve of the plot of Bhattacharya Coefficients v/s search location in pixels is the location of bottom edge of the rectangular sub- region, as shown in Fig. 4(c) ‘ (ii).The segmented region with the bottom edge precisely fitted is shown in the Fig. 4(b) ‘ (ii).

Fitting of Right edge: The Precise location of the right edge of rectangular sub-region is searched from the left edge of the sub-region in horizontal right direction. Bhattacharya Coefficient at each search location is noted down. The minimal point (x = 41 pixels) of the steepest rising curve of the plot of Bhattacharya Coefficients v/s search location in pixels is the location of right edge of the rectangular sub-region, as shown in Fig. 4(c) ‘ (iii).The segmented region with the right edge precisely fitted is shown in the Fig. 4(b) ‘ (iii).

Fitting of Left edge: The Precise location of the left edge of rectangular sub-region is searched from the fitted right edge of the sub-region in horizontal left direction. Bhattacharya Coefficient at each search location is noted down. The minimal point (x = 39 pixels) of the steepest rising curve of the plot of Bhattacharya Coefficients v/s search location in pixels is the location of left edge of the rectangular sub- region, as shown in Fig. 4(c) ‘ (iv).The segmented region with the left edge precisely fitted is shown in the Fig. 4(b) ‘ (iv).

Crudely Segmented tumor Fixing of top edge Fixing of bottom edge Fixing of right edge Fixing of left edge

(a) (b-i) (b-ii) (b-iii) (b-iv)

(c-i) (c-ii) (c-iii) (c-iv)

Fig. 4: Locating of top, bottom, right and left edges of the crudely segmented sub-region: Case-3 Tumor (from left to right). (a) Crudely Segmented Tumor Region, (b) Output images after the four edges are fixed, (c) Plots of Bhattacharya coefficient v/s search locations in pixels.

4.2.1. Outputs of Crude and Precise Segmentation for the three cases

Fig. 5 (a) and Fig. 5 (b) show the outputs of Crude and Precise detection, respectively, for the three cases of tumors. It is observed that the output of Crude Segmentation is a sub-region that does not contain tumor entirely and exactly. Whereas, the output sub-region of Precise detection contains tumor entirely and exactly.

(a-i) (a-ii) (a-iii)

(b-i) j(b-ii) (b-iii)

Fig. 5: Segmentation of Tumor Regions. Crude Segmentation. (b) Precise Segmentation.

4.2.2. Comparison of Bounding Box position of our algorithm and Nilanjan Ray’s algorithm

The center of bounding box rectangle can be used as a position of initialization of level sets, for finding a more accurate boundary of brain tumors. Hence, it is essential that, the bounding box should localize the tumor, entirely and exactly. It is observed from the Fig. 6(a) that the position of Bounding Box (Red) using Nilanjan Ray’s algorithm [24] has not covered tumor, entirely and exactly, for the three different cases of tumors. Whereas, that in our algorithm, Yellow Bounding Box, in Fig. 6(b) has exactly circumscribed the entire tumor.

(a-i) (a-ii) (a-iii)

(b-i) (b-ii) (b-iii)

Fig. 6: Detected Tumor Regions by Bounding Box. (a) Using Nilanjan Ray’s algorithm (Red Bounding Box), (b) Using our algorithm (Yellow Bounding Box)

4.2.3. Performance of Detection Algorithms

To quantify the performance of our algorithm we use Dice coefficient [26] given by equation (2):

(2)

where, R is the set of the pixels of a bounding box around the true abnormality, found by an expert radiologist and S is set of pixels of the bounding box found by our algorithm. The modulus sign appearing in the Dice coefficient expression denotes cardinality (number of pixels in this case) of a set. In general, the Dice coefficient is a value between 0 and 1, with 1 being the ideal segmentation, S = G. The closer the Dice coefficient is to unity, the better the segmentation is. Fig. 7 shows encouraging Dice coefficient values for six tumor cases of brain MRI data taken from the results of our algo-rithm compared to that of Nilanjan Ray’s algorithm.

Fig. 7: Performance of Detection Algorithms

4.2.4. Percise Detection using plots of Standard Deviation and Mean Intensity – Distance

Similar to Bhattacharya coefficient (BC), we tried to detect dissimilarity using Standard Deviation-distance (SD_dist) and Mean Intensity’distance (MI_dist) between a sub-region in one hemisphere of the brain with respect to its reflection about the axis of symmetry in the other hemisphere. Further, SD_dist and MI_dist are plotted v/s search position of edges in pixels.

The locations of top, bottom, right and left edges of the crudely segmented tumor sub-region as shown in Fig. 8(a) is located as shown in Fig. 8(b) by referring the minima in Bhattacharya Coefficient plots of Fig. 8(c), respectively. Similarly, the maxima in Standard deviation’distance plots of Fig. 8 (d), and Mean Intensity-distance plots in Fig. 8 (e), can also be used to determine precise locations of four edges of the segmented sub-region. The dots in the each plot show the positions of edges placed by an expert radiologist. It can be observed from the plots of Fig. 8 that, the minima in Bhattacharya Coefficient plots dictate the positions of the edges more precisely than that of maxima in Standard deviation’distance plots or Mean Intensity-distance plots.

Crudely Segmented tumor Fixing of top edge Fixing of bottom edge Fixing of right edge Fixing of left edge

(a) (b-i) (b-ii) (b-iii) (b-iv)

(c-i) (c-ii) (c-iii) (c-iv)

(d-i) (d-ii) (d-iii) (d-iv)

(e-i) (e-ii) (e-iii) (e-iv)

Fig 8: Fixing of top, bottom, right and left edges of the crudely segmented sub-region: Case-1 Tumor (from left to right). (a) Crudely Segmented Tumor Region, (b) Output images after the four edges are fixed, (c) Plots of Bhattacharya Coefficient v/s search locations, (d) Plots of Standard Dev-iation-distance v/s search locations of edges, (e) Plots of Mean Intensity-distance v/s search locations of edges.

5. Conclusion

The localization of brain tumors by a bounding box using the proposed approach is more precise than that of other histogram-based bounding box techniques. The brain tumors are circumscribed by bounding box entirely and exactly. The minima in Bhattacharya Coefficient plots dictate the positions of the edges more precisely than that of maxima in Standard deviation ‘ distance and Mean Intensity – distance plots.

The approach is more simple and straight-forward and can be carried on single MRI slice. This technique does not need image registration; a training set of labeled images. It can be implemented in real time. In addition, the center of bounding box rectangle can be used as a seed or initialization position of level sets, for finding a more accurate boundary of brain tumors using active contours.

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