Detection of bone contours in x-ray images is an important step in the computer analysis of medical images. Analog X-ray images are characterized by low contrast ratio value and high variability of their optical properties. Therefore classical segmentation algorithms based on homogeneity criteria are not applicable. In this paper we propose an approach for automatic bone contours detection which does not require homogeneity of regions. This method is based on accurate edge fragments detection and elimination of discontinuities between them. We have dened the criteria for calculating numerical characteristics of the quality of image contours detection. The obtained results are used for diagnosis of abnormalities and diseases of the detected object.
Digital images are currently widely applied for disease diagnostics in medical science. Using Roentgen radiation for radiograph (X-ray image) acquisition, which allows detecting fractures, bone abnormalities and other diseases, is one of the most widely-spread and cost eective non-invasive medical monitoring methods. However, most of the papers on medical images segmentation are focused on CT- and MRI images. In this paper we present the method developed for X-ray images analysis.
We concentrate on the problem of automatic segmentation of bone structures in X-ray images. Low contrast ratio value of the analog X-ray images along with their optical properties complexity is one of the major challenges in solving this problem. In particular, objects in the radiography images have irregular texture and intensity. Consequently, traditional segmentation techniques based on thresholding, region growing, clustering, watershed transformation etc. cannot be applied, since their implementation requires exact regions homogeneity test. Deformable models (snakes, active contour models) can be used for X-ray image segmentation, but an accurate initial estimate is necessary to this end, otherwise the segmentation result can be unacceptable.
In this paper we propose an approach for automatic bone contours detection which does not require homogeneity of regions. It can be used for joint recognition in X-ray images. This method is based on accurate edge fragments detection and elimination of discontinuities between them. We have dened the criteria for calculating numerical characteristics of the quality of image contours detection. The obtained results can be applicable for diagnosis of abnormalities and diseases of the detected object. 2
As discussed in Section 1, classical segmentation algorithms based on
homogeneity criteria are not applicable. In paper [
Some techniques of contours extraction are based on using 2D template of
the desired object or some other a priori knowledge about it [
However, the methods which use templates have signicant limitations. They
are not applicable for detecting objects with strong shape distortion. And in cases
of medical images such objects are of particular interest. In the article [
The paper [
We propose an approach which does not use a priori information about the shape of the object. This allows us to avoid problems arising from the strong distortion of the shape. 3
I = fI(x; y) 2 [0; 255] j 1 < x
M; 1 < y
N g :
Before starting the image undergoes light blurring to eliminate spot noise.
The best results were obtained using bilateral ltration algorithm [
At this stage the image gradient rI is computed, for the purpose we suggest
Kirsch operator [
We further proceed with an image, which is element-wise multiplication of gradient magnitude and GVF magnitude, we denote it by G1 (Fig. 3, a). For this image, an estimated binarization threshold T is computed. Edge thinning operation is then conducted by using GVF direction values. We denote the resulting image by G2 (Fig. 3, b).
The next stage is nding binarization threshold for the image G2. We nd it in T form, where denotes a coecient in the range (0; 1]. For all involved, binarization threshold of the image G2 with T is conducted. The obtained binary image contains fragments of the object boundaries. For merging these fragments into contours special algorithms have been devised. After nishing the discontinuities elimination procedure we get an image with the target contours. The quality of obtained contours detection is then numerically estimated, as dened within the research. After computing the estimates for various threshold values it remains to choose value such that the estimate is the best, we denote it by . Further processing involves contours obtained with binarization threshold T .
The resulting contours are rened with active contour method [
Pre-processing Let v = [u(x; y); v(x; y)] denote gradient vector ow eld of input image. and jvj are computed using the formulas: vdir 1. Brightness gradient magnitude is calculated for each pixel of the image
Gb(x; y) = max(jG1;x(x; y)j; jG1;y(x; y)j): Directional derivatives G1;x, G1;y are regarded as discrete analogs of dierentiation operator:
G1;x(x; y) = G1(x + 1; y)
G1(x
G1;y(x; y) = G1(x; y + 1) G1(x; y 2. Target threshold is calculated according to formula 1; y);
1): T
N M
P P G1(x; y) Gb(x; y) = y=1 x=1
N M P P Gb(x; y) y=1 x=1 : (1) 3.3
Chaining Let Gbin denote an image obtained by binarizing G2 with some threshold. This image contains fragments of edges. We propose an approach of chaining the fragments, i.e. elimination of discontinuities between the fragments that belong to one contour. Chaining algorithm includes two stages. At the rst stage, we eliminate discontinuities for pairs of pixels. At the second stage, we process pixels left unpaired. Both stages run iteratively. At each iteration we remove discontinuities whose length is less than a dened constraint K. We increase K at each iteration.
Let U (p) denote a set of pixels of a boundary which are adjacent to p (i.e. pixels for which Gbin(pi) = 1), jU (p)j denotes cardinality. Pixels of the boundary are assumed 8-adjacent: jU (p)j 8, denotes Euclidean distance between the points. We distinguish 3 types of discontinuities in boundaries (Fig. 4): 1. a point, for which jU (p)j 2. a point, for which
1
U (p) = fp1; p2g : (p1; p2) = 1; x1 = x2 _ y1 = y2
U (p) = fp1; p2; p3g : (p1; p2) = 1; (p1; p3) = 1; x1 = x2; y1 = y3 Let p and q denote discontinuity points, r a point adjacent to p. We dene u as a vector codirectional with r-to-p vector. Coecient d denotes deviation range between points q and p in the u direction (see Fig. 5).
Knowing u direction and d value, we dene vectors and ! to limit area of searching the discontinuity point associated with p point: x = ux cos ( d)
uy sin ( d); y = ux sin ( d) + uy cos ( d); !y = ux cos d
uy sin d; !y = ux sin d + uy cos d:
If q is located between limiting vectors and ! with origin p (2), then we attempt to eliminate discontinuity between p and q.
!xty !ytx 0; tx y ty x < 0; (2)
Chaining implies nding a set of 8-adjacent pixels that provide 8-adjacency of p and q, i.e. nding a path between p and q.
For path search we apply algorithm A , which is an extension of Dijkstra’s algorithm demonstrating acceptable results on a plain grid. We apply following heuristics: the entire image is traversable; the cost of point p traversal is jrI(p)j value multiplied by 1; the cost of point-to-point transfer includes Euclidian distance and absolute dierence of gradient values; the next point selection relies on heuristic evaluation of distance to the target.
The range of jrIj values is preliminary scaled. The larger the gradient values range, the more precise obtained curve retraces the boundary of the target object. Some regions of the image contain densely spaced bounds of two dierent objects. In that case the algorithm can jump to another object’s bound due to gradient identity. Therefore it’s important to t the scaling coecients. In this paper we suggest mapping jrIj values to [0; 10].
Let us denote found path by = f igiL=1, average gradient value of the entire image by , path cost by : = 1. Path cost is more than conditional cost 0 = L :
Parameter is directly-proportional to restriction K on length of the discontinuity being removed;
does not intersect already existing fragments of bounds on the image Gbin (Fig. 6, left);
If the conditions hold, we assert that points of the image Gbin (Fig. 6, right). belong to target bounds on For an unpaired point of discontinuity, the curve is grown following the gradient. Next point of the curve is chosen in a direction orthogonal to gradient in the previous point. We halt growing the curve if we reach a pixel for which at least one of the following conditions holds: 1. it is an element of some bound fragment (Fig. 7, left): 2. it is a border pixel of the image (Fig. 7, right):
(x; y) : Gbin(x; y) = 1; (x; y) : x 2 f1; M g _ y 2 f1; N g:
We do not consider the curves whose length exceeds the constraint K. If condition (3) holds for , then we assert that points of belong to target bounds on the image Gbin. (4) (5) Let W denote a set of image I pixels whose intensity values exceed binarization threshold found by applying Otsu’s algorithm to I.
We further denote bounded region by , number of the region pixels by j j, W cardinality within region by w( ), average pixels intensity value of image I in region by avg( ), number of binary image A pixels whose intensity value exceeds binarization threshold by v(A): w( ) =
X Ibin(p); p2 1
X I(p); j j p2 avg( ) = p2S v(A) =
X A(p); S = [1; M ] [1; N ]: quality with
Our prime interest is in the regions i such that: 1. avg( i) exceeds the threshold found by applying Otsu’s method to image I; 2. jw( i) j jj < ".
i. We estimate edge detection n = S
i=1 E = w( ) v(Ibin) 1 v(G v(Ibin)
Ibin) 1
j j N M w( ) v(Ibin) ; (6) where G denotes binary image after applying chaining algorithm. We adjust threshold for the best contour detection. To that end, we use suggested numerical estimate. We propose an algorithm of threshold computation in the form T as follows.
For all in (0; 1] with some increment, we execute the following steps:
2. obtained binary image undergoes chaining procedure, the resulting image is
G; 3. edges of the objects are extracted on the image G; 4. obtained set of contours is numerically estimated by E .
After computing E we search
: = argmax E : The result of nal edge detection is a set of contours detected with threshold T .
To rene the detected edges, active contour method can be applied. The suggested detection method assures that small iterations number of active contour method is required. 4
We tested the algorithm for X-ray images of knee and elbow joint in lateral and coronal view, with various resolution, quality and distortion of bones. We have tested about 100 X-ray images provided by Rostov State Medical University.
The eciency evaluation results of the proposed method are presented in Table 1. Contours on 74% of test images were successfully extracted, despite the variations in shapes, sizes and shape distortion of the bones (Fig. 8). 14; 2% of the images are marked as a partial success (Fig. 9, a, b). The other 11; 8% do not have acceptable results (Fig. 9, c). Failed samples contain such artifacts as noise or many false borders, caused by the process of obtaining analogue images. The paper introduces the method of automatic detection of bone contours in medical X-ray images. It is based on boundary fragments detection with further chaining them to contours. The method does not require homogeneity, the lack of which is typical for X-ray images. Numerical estimate of edge detection quality is also proposed.
Algorithm specicity provides an opportunity to make good use of parallelizing the computation (in particular on the stages of chaining and threshold adjusting). This implies high-speed performance of the developed program.
The method was tested on a set of medical images provided by Rostov State Medical University.
In contrast to methods based on template matching, the suggested approach is applicable for detecting the objects of badly distorted shape (bone fractures, ail joint etc). Consequently, it is suitable not only for health status evaluation but for classifying defects in joints within health screening as well.