Method for fast and accurate segmentation processing from prior shape

Method for fast and accurate segmentation processing from prior shape : application to femoral head segmentation on X-Ray images Ramnada Chava,b,c , Thierry Cressona,b,c , Claude Kauffmanc,d and Jacques A. de Guisea,b,c,d a Laboratoire

de recherche en imagerie et orthopédie, Hôpital Notre-Dame, 1560 rue Sherbrooke Est, Montréal, Canada; b Ecole ´ de technologie supérieure, 1100 rue Notre-Dame Ouest, Montréal, Québec, Canada; c Centre de recherche du centre hospitalier de l’Universit´ e de Montréal, Montréal, Québec, Canada; d Universit´ e de Montréal, 6128 succursale Centre-ville, Montréal, Canada ABSTRACT This paper proposes a prior shape segmentation method to create a constant-width ribbon-like zone that runs along the boundary to be extracted. The image data corresponding to that zone is transformed into a rectangular image subspace where the boundary is roughly straightened. Every step of the segmentation process is then applied to that straightened subspace image where the final extracted boundary is transformed back into the original image space. This approach has the advantage of producing very efficient filtering and edge detection using conventional techniques. The final boundary is continuous even over image regions where partial information is missing. The technique was applied to the femoral head segmentation where we show that the final segmented boundary is very similar to the one obtained manually by a trained orthopedist and has low sensitivity to the initial positioning of the prior shape. Keywords: Segmentation, Prior Shape, Straightening, Ribbon-Like Zone, Image Transformation, Boundary Extraction

1. INTRODUCTION The task of identifying boundaries of structures of interest from an underlying background, defined as image segmentation, is one of the most important and difficult steps in the process of computer reconstruction and analysis from radiographic images. Many difficulties are inherent to the images themselves: structure boundaries are not always well delineated; they frequently appear blurred, broken or discontinuous in the images; there is often a large amount of spurious edges due to feature superposition. Typically, segmentation problems are decomposed into a three-step process1 : 1) pre-processing, 2) feature extraction and 3) classification (Fig.1). For the computer analysis of bone structures from radiographic images, the position and orientation of the feature boundaries have to be determined with an accuracy that relies on the precision of each individual step.

Figure 1. Image processing steps for segmentation in a straightened subspace from prior shape. Further author information: (Send correspondence to Ramnada Chav) Ramnada Chav: E-mail: [email protected], Telephone: 1 514 890 8000 (28720)

Medical Imaging 2009: Image Processing, edited by Josien P. W. Pluim, Benoit M. Dawant, Proc. of SPIE Vol. 7259, 72594Y · © 2009 SPIE CCC code: 1605-7422/09/$18 · doi: 10.1117/12.812459 Proc. of SPIE Vol. 7259 72594Y-1

The goal of image pre-processing is to reduce unwanted noise and enhance contrast between regions of different intensities. Noise reduction is generally done by encouraging smoothing within regions of similar intensity while preventing it across regions with intensity discontinuities (edges). While most conventional spatial filters (linear or statistical) have the advantage of being efficient in computational time, they usually tend to smooth edges out or displace them as shown in Fig.2c. To prevent edge displacements, the use of non-linear isotropic diffusion filters and anisotropic diffusion filters2 is preferred as they are more efficient in noise reduction, preservation of interregional discontinuities and contrast enhancement by considering the position and orientation of the intensity discontinuities present in an image. Feature extraction consists in extracting characteristics that will help isolate the structure of interest from its background. A common feature used for segmentation is edge detection which consists in finding all boundaries contained in the image. The positional precision of the edge detection is very dependent on the quality of the pre-processing step. Differential spatial filters are often used for edge detection. They are generally decomposed to detect horizontal and vertical edges independently (following x-axis and y-axis of the image). The norm is usually taken to get the amplitude of the edges of various orientations. The classification step consists in finding with accuracy the boundary that separates the structure of interest from the background by relying on the extracted features. Most methods used in medical image segmentation3 are based on Active Contours4 , Level Set5 and Active Shapes6, 7 techniques. There are three main limitations to these techniques : 1) they are iterative and sensitive to the initializations; 2) they have a high tendency to be attracted to noise and spurious edges or to leak into neighboring structures; and 3) they often depend on a series of parameters such that fine tuning can highly influence the final accuracy results. A solution is to use a prior shape to guide the final segmentation shape over a region where no features are found.

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Figure 2. Effect of spatial filter on intensity discontinuities by filtering without respecting the position and orientation of intensity discontinuities : Synthetic circle with gaussian noise. (a) Original synthetic image. (b) Synthetic image with gaussian noise added. (c) Filtered image using a median filter and a specific threshold.

In order to simplify segmentation steps and to create an optimal region of interest, a partial image transformation to a straightened subspace is introduced. As shown in Fig.3, the central processing block still involves the three steps of a typical segmentation problem. However, they are now specifically designed to process images with mostly oriented features. Segmentation Process Image Straightened subspace

Preprocessing

Feature Extraction

Classification

Prior shape

Segmentation results to Original image space

Segmented Image

Figure 3. Image processing steps for segmentation in a straightened subspace from prior shape.

Proc. of SPIE Vol. 7259 72594Y-2

Previous authors8, 9 have used the polar coordinate transform for the extraction of circular features. This work suggests instead to generalize the technique and complement it with an opened or closed prior shape of any geometry. In section 2, the image transformation for the straightened subspace is presented. Section 3 shows how the straightened subspace can simplify and accelerate the segmentation process. In section 4, the method is used to extract the boundary of a femoral head in a radiograph using the straightened image technique. A conclusion follows in section 5.

2. IMAGE TRANSFORMATION TO THE STRAIGHTENED SUBSPACE The generation of a straightened subspace requires a prior shape with its known position and orientation in the image. Such information can be provided in several ways using statistical models, mathematical models, manual initializations, etc. In this work, the straightened subspace image is created using coordinates transformation of the image based on a curvilinear prior shape given by the curve (ζ) : (1) ζ = { Pi (xi , yi ), i = 1, ..., n} − → ∀Pi = (xi , yi ) ∈ ζ, a corresponding normal vector Ni can be calculated: − → Ni = (N xi , N yi )

(2)

A transformation matrix Tm allowing the passage of the coordinates from the original image to the straightened subspace image, or inversely, can be calculated by : − → − → Tm (xi , yi ) = (N xi · Av + xi , N yi · Av + yi )

(3)

− → where Av is an acquisition vector defining the width and the resolution of the ribbon-like zone. For example if − → we would like to take 10 pixels each side of the prior shape with a resolution of 0.5 pixels the Av will go from -10 to 10 with a step of 0.5. The resulting straightened subspace image width will be of the same size as the length − → of Av. The straightened subspace image (SI) is then created by using Tm . SI = I(Tm )

(4)

Once the straightened boundary (SB) of the structure of interest is obtained from the straightened subspace image, the coordinates of the final boundary (F B) in the original image space is found by using the same transformation matrix Tm . F B = Tm (SB) (5)

3. WORKING ON STRAIGHTENED SUBSPACE IMAGE The resulting straightened subspace image corresponds to a ribbon-like zone around the structure of interest where the boundary to extract is now mostly oriented along one direction. This particularity has two advantages: 1) it considerably simplifies the segmentation process now that the structure of interest to be extracted is mostly oriented in a single direction (horizontally or vertically) as shown in Fig.4; and 2) it greatly reduces the number of pixels to be processed, therefore decreasing the computational time (Fig.5). The reorientation of the boundary of interest to be mostly horizontal or vertical allows great simplification of all segmentation processing steps and still maintains precision and robustness for segmentation results by using fast conventional techniques and produce results comparable to those provided by more complex techniques. The synthetic circle from the example in Fig.2 is segmented in Fig.4 using the straightening subspace. The straightened subspace allows an effective image filtering that preserves the location and the sharpness of the image boundary. In the example of Fig4d, efficient filtering is realized using a simple asymmetric and


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Figure 4. Segmentation process by taking advantage of the straightened subspace : Synthetic circle with gaussian noise (comparison with Fig.2). (a) Original synthetic image. (b) Synthetic image with gaussian noise, prior shape (red dashed line), acquisition vector (blue solid line) and ribbon-like zone (highlighted in yellow). (c) Conversion of the noisy image to the straightened subspace using the prior shape (red dashed line) and the acquisition vector (blue solid line). (d) Boundary of the circle (green solid line) extracted from the filtered noisy image in the straightened subspace by using conventional asymmetric median filter. (e) Segmentation result : conversion of the extracted boundary in the straightened subspace back to the original image (green solid line).

oriented median filter (allowing parallel filtering) to simultaneously reduce noise and maintain a high precision along the interregional frontier, resulting in the filtered image. In the filtered image, the boundary is mainly oriented in one direction. Therefore, edge detection can be performed only along that single direction. The complement of the resulting image provides a cost map, where low values correspond to the edges of the image. The last step in the segmentation process is the classification of the extracted features. The cost map combined with a minimal-path algorithm, as explained in Mortensen et al.10 and Vincent11 , were used to extract the

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Figure 5. Relevance of the shape prior in the specification of a region of interest. Thigh zone of a patient on x-ray front view image for which a generic 3D model of a femur must be registered. (a) Typical rectangular ROI (highlighted in yellow) that one would normally use; the image counts more than 500,000 pixels and the zone encloses about 175,000 pixels. (b) More efficient ROI defined by a ribbon-like zone (highlighted in green) running along an approximate boundary of the femur; less than 50,000 pixels are involved (71% reduction compared to the typical rectangular ROI). The boundary is defined as the projected 2D contours of a 3D bone model whose position, orientation and size are roughly approximated.


main boundary of the straightened subspace image. This algorithm efficiently extracts a solution from the cost map to provide a low-cost continuous path using dynamic programming. There are three main advantages in using the minimal-path technique for the classification step: 1) classification can be done in a single step; 2) only one parameter for linearity needs to be adjusted; and 3) extrapolation over regions with broken edges is implicit (Fig.4e).

4. RESULTS AND DISCUSSION This method is applied to extract the femoral head boundary as shown in Fig.6. The main problems encountered during the segmentation of the femoral head are the non-uniform image blur and the discontinuous feature boundaries. Such problems tend to plague the conventional active contour methods and lead to leakage in neighboring structures such as the acetabulum. A retroprojection of a generic 3D model of the femoral head is roughly initialized in the image by a user, using a 3 handles MLS technique12 , to create the prior shape used for the segmentation process (Fig.6). The exact positioning of the generic model has minimal influence on the accuracy of the final segmentation. Based on that prior shape, a straightened image is generated and the segmentation process is applied following the method described in the previous section. After the completion of the segmentation process, the resulting segmentation is projected back to the original image space, using Eq.5. The final result is displayed in Fig.6e (green solid line). Images acquired from 25 subjects were used in order to evaluate this method. In each case, the semi-automatic segmentation of the femoral head was initialized by deliberately placing a 3D generic model of the femoral head at an approximate distance of 3mm off center in order to assert the robustness of the segmentation method (some results are presented in Fig.7). The results were then compared to the boundary of reference that was manually delineated by a trained orthopedist. The local segmentation error is thus defined as the distance between the boundaries from the semi-automatic method and the reference boundaries. This distance is measured along the normal direction of the reference boundary. The mean, median and maximum errors (in mm) are computed for the entire reference boundary of a subject. The relative error is the ratio between the error and the diameter of the femoral head. Table I presents the combined results for 25 different subjects. Table 1. Statistical analysis of the segmentation errors.

Distance [mm] Relative error

Mean 0.45±0.26 1.15%

Median 0.41±0.27 1.06%

Max 1.23±0.83 3%

5. CONCLUSION The method presented in this paper relies on a straightened subspace image representation that greatly simplifies image processing. It provides both segmentation accuracy and robustness at a low computational cost. Applying the method on the femoral head generates segmentation results that are very similar to expert manual segmentation. The results demonstrate a great robustness to the contour initialization. This method could be applied to the difficult task of automatic contour detection of specific structures in full-body radiographs.

ACKNOWLEDGMENTS This study was supported in part by the Natural Sciences and Engineering Research Council of Canada, the Canada Research Chair in 3D Imaging and Biomedical Engineering and Biospace med, France. We also thank Benoit Godbout, Dominic Branchaud, Caroline Lau and Karine Morin for their great support.


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Figure 6. Segmentation of femoral head using straightened subspace technique. (a) Femoral head on X-ray frontal image. (b) Frontal image with retroprojection of the generic 3D model as prior shape (red dashed line) with some acquisition vector (blue solid line) and the ribbon-like zone (highlighted in yellow). (c) Straightened image with prior shape (red dashed line) and normal vector (blue solid line). (d) Extraction of the boundary of the femoral head (green solid line) in the straightened subspace using minimal path technique. (e) Result of the segmented femoral head (green solid line) compared to the prior shape (red dashed line) in the original image

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Figure 7. Segmentation results on different femoral head. Prior shape is in dashed red and segmentation results in solid green.
