Texture Analysis of Proximal Femur Radiographsfor Osteoporosis Assessment

TATI RAJAB MENGKO and J. TJANDRA PRAMUDITODepartment of Electrical Engineering

Bandung Institute of TechnologyJalan Ganesha 10, Bandung 40132

INDONESIA

Abstract: - The osteoporosis assessment can be done by observing and analyzing the trabecular pattern in proximal femur. To reduce variability, a machine vision system based on texture analysis using Gabor filter is introduced. Multi-channel filtering implemented by Gabor function, or Gabor filter, is capable to mimics characteristics of the human visual system. In the assessment of osteoporosis, Gabor filter is used to calculate features from trabecular pattern recorded on radiographs of proximal femur. The extracted features represent the quality or structure of the bone, better quality represents better bone strength, lower quality leads to low bone strength and could be suspected as osteoporosis. Extracted features from trabecular pattern recorded in proximal femur radiographs by Gabor filter match with their predetermined Singh index.

Key-Words: - texture analysis, Gabor filter, osteoporosis, proximal femur, trabecular pattern, radiographs

1 IntroductionWith the better life expectancy the risk of facing diseases caused by aging process is increasing. One of the diseases is osteoporosis. Osteoporosis is characterized by an absolute decrease in the amount of bone to a level below that required for mechanical support of normal activity and by the occurrence of non-traumatic skeletal fracture [1]. In other word, osteoporosis is very related to the strength of bone. Optimal estimation of bone strength could probably be achieved if both bone structure and mass could be measured together [1]. Bone mass can be measured by Bone Mineral Densitometry (BMD) technique using various mode such as ultrasound or Dual Energy X-ray Absorptiometry (DEXA). For the time being DEXA is considered as a gold standard to detect osteoporosis. Bone structure can be estimated by observing the trabecular pattern in proximal femur recorded on radiograph. The use of trabecular pattern change for the diagnosis of osteoporosis was first proposed in the 1960s using radiographs of proximal femur. The diagnosis was known as Singh Index grading system but always been considered too variable for diagnosis or epidemiology [2],[3],[4],[5]. Because of the availability of x-ray instrumentation in Indonesia and the expensive price of DEXA equipment quite a number of physician use direct observation of proximal femur radiograph to assess

osteoporosis. On radiographs, cancellous (trabecular) bone structure appears as a distinct pattern. Figure 1 show the principal trabeculae in proximal femur which are considered as texture. There are two major trabeculae, the principal compressive trabeculae and the principal tensile trabeculae.

(a) (b)

Fig. 1 (a). Principal Compressive Trabeculae (b). Principal Tensile Trabeculae

To solve the variability problem of Singh index grading system we proposed the machine vision system for osteoporosis assessment. Texture analysis using Gabor filter technique will be applied to extract the features of trabecular pattern recorded on proximal femur radiographs. Features extraction of proximal

femur trabecular pattern using other texture analysis technique, discrete wavelet transform (DWT), has been performed with quite promising result [6]. The extracted features will represent the quality or structure of the bone, better quality represents better bone strength, lower quality leads to low bone strength and could be suspected as osteoporosis. The extracted features of the samples, in the form of energy, is then compared with their corresponding Sing index determined by physician. This paper is organized as follows, section 2 and 3 give a brief theory of texture analysis and human vision system and Gabor filter respectively. Preprocessing of radiographs is described in section 4 and features extraction method is described in section 5. In section 6 we present the experimental result and we put the conclusion of this paper in section 7.

2 Texture AnalysisTexture analysis algorithm has a wide range application from random field model to multi-resolution filtering. Multi-resolution filtering or multi-channel is an effective consideration in the field of texture analysis and could mimics characteristics of the human visual system (HVS) [7]. Research has shown that the HVS generates a multi-resolutional decomposition and the Gabor function can be implemented as a multi-channel filter [7]. Multi-resolution filtering technique based on Gabor filter will be used in texture analysis of trabecular pattern in proximal femur. The application of Gabor filter to calculate features from textured images is motivated by capability of the elementary Gabor function to simultaneously minimize the two dimensional uncertainty in space and frequency [7]. Gabor filter can be used as a model of simple cell receptive field in some mammalians visual cortex [8]. In its development, Gabor filter are used in texture analysis and feature extraction [9], [10]. Gabor feature has been used in several image analysis applications as in texture classification and segmentation [11], [12]. The Gabor filter is applied to classification of osteoporosis level based on the change of trabecular pattern. Classification performed based on features extracted by Gabor filter in the form of energy. The classification result then compared with Singh index determined by physician.

3 Gabor FilterSpatially, a Gabor function is a Gaussian modulated sinusoid. The 2-d Gaussian has an aspect ratio of σx/σy.

The complex exponential has a spatial frequency of F an orientation of θ. A complex Gabor filter represented as a 2-d impulse response is

(1)

Fig. 2 Impulse response of 2-D Gabor filter

Considering that x-axis of the Gaussian has the same orientation θ as the frequency then rotation in x-y plane provides for any arbitrary orientation of filter [9]. The corresponding representation in the spatial-frequency domain is

(2)

A rotation can be used to obtain any direction in the u-v (spatial-frequency) as in the x-y (spatial) plane. There are six parameters that must be set when implementing this Gabor filter: F, θ, σx, σy, BF, and Bθ

[9]. The frequency and angular bandwidths (BF, Bθ) usually set as a constant values. The frequency (F) and orientation (θ) define the center of the filter. The unknown σx and σy are determined by following equations,

(3)

(4)

The variable σx is determined by setting the frequency cut-off to –6 dB variable σy is determined by setting the frequency cut-off in angular direction to –6 dB as well.

In this paper we used frequency bandwidth (BF) of one octave, center frequency spacing (SF) of one octave, angular bandwidth (Bθ) of 30o and 45o, and angular spacing (Sθ) of 30o and 45o. The shape of Gaussian used are an elliptical (Bθ = Sθ) and circular (σx= σx) [6]. The 30o angular bandwidth agrees more closely to physiologically derived HVS characteristics and 45o angular bandwidth is used as a comparison as researchers used this in their research [13].

4 Radiographs PreprocessingBefore applying to Gabor filter, the radiographs are preprocessed to achieve better image quality. The radiographs are preprocessed with a series of filter like high-pass, wiener and median filters. The block diagram of preprocessing of radiographs is as follows

Fig. 3 Preprocessing block diagram

Figure 4 shows the example of original radiograph and the result of preprocessing.

(a) (b)

Fig. 4. (a) Original radiograph, (b) Result of preprocessing

5 Features ExtractionExtraction of Gabor features was performed using energy calculation as follows

(5)

for Gabor images x(m,n) with 1 ≤ m ≤ M and 1 ≤ n ≤ N. Gabor features were calculated on certain region of interest (ROI) of proximal femur known as Ward’s triangle and femoral neck. The Ward’s triangle is the

region that is most sensitive to bone mass lost [4]. Figure 5 shows the ROI used in this paper.

Fig. 5 Region of Interest (ROI).

Feature images produced by applying ROI images to Gabor filter in several orientations are shown in Figure 6. Gabor filter used to produce these images was set to angular spacing of 30o with orientation from 0o to 150o and center frequency of √2/24.

(a) (b)

(c) (d)

(e) (f)

Fig. 6 Gabor feature images at several orientations (a). 0o, (b). 30o, (c) 60o, (d). 90o, (e). 120o, and (f). 150o.

6 Experimental ResultIn this paper we used four different trabecular patterns of 55 radiographs. The four trabecular patterns are shown in Figure 7.

HPF

Wiener

MedianFilter

(a) (b)

(c) (d)Fig. 7 Four different trabecular pattern: (a). Grade 6 (b). Grade 5 (c). Grade 4, and (d) Grade 3.

This trabecular pattern has been examined by physicians and classified as grade 6 to grade 2 according to Singh index. The higher grade means better bone condition. The feature extracted from Gabor features by energy calculation is then compared to predetermined Singh index to investigate the capability of Gabon features to assess the degree or level of osteoporosis. The extracted features in the form of energy by applying Gabon filter in elliptical shape with 30o and 45o angular bandwidth with orientation from 0o to 150o

and center frequencies of

for 3 image samples with Singh index of 3, 4 and 5.

Feature extraction in the form of energy for image samples with Singh index of 3, 4 and 5 are as follow

Table 1 Feature extraction (energy) with Bθ = Sθ = 30o (Singh index = 3)

0o 30o 60o 90o 120o 150o

F0 0.32 0.30 0.32 0.30 0.32 0.30F1 0.29 0.01 0.01 0.18 0.01 0.01F2 0.02 0.01 0.01 0.01 0.01 0.01F3 0.05 0.04 0.03 0.04 0.03 0.04

F4 0.34 0.34 0.34 0.30 0.34 0.34F5 0.34 0.34 0.34 0.34 0.34 0.34F6 0.34 0.34 0.34 0.34 0.34 0.34

Table 2 Feature extraction (energy) with Bθ = Sθ = 45o (Singh index = 3)

0o 45o 90o 135o 180o 225o

F0 0.32 0.33 0.30 0.33 0.32 0.33F1 0.29 0.04 0.18 0.06 0.29 0.04F2 0.02 0.00 0.01 0.00 0.02 0.00F3 0.05 0.04 0.04 0.05 0.05 0.04F4 0.34 0.34 0.30 0.34 0.34 0.34F5 0.34 0.34 0.34 0.34 0.34 0.34F6 0.34 0.34 0.34 0.34 0.34 0.34

Table 3 Feature extraction (energy) with Bθ = Sθ = 30o (Singh index = 4)

0o 30o 60o 90o 120o 150o

F0 0.42 0.43 0.41 0.43 0.41 0.43F1 0.25 0.01 0.01 0.29 0.01 0.01F2 0.02 0.01 0.01 0.02 0.01 0.01F3 0.05 0.04 0.05 0.06 0.05 0.04F4 0.40 0.45 0.45 0.45 0.45 0.45F5 0.45 0.45 0.45 0.45 0.45 0.45F6 0.45 0.45 0.45 0.45 0.45 0.45

Table 4 Feature extraction (energy) with Bθ = Sθ = 45o (Singh index = 4)

0o 45o 90o 135o 180o 225o

F0 0.42 0.43 0.43 0.43 0.42 0.43F1 0.25 0.04 0.29 0.06 0.25 0.04F2 0.02 0.00 0.02 0.00 0.02 0.00F3 0.05 0.04 0.06 0.04 0.05 0.04F4 0.40 0.45 0.45 0.45 0.40 0.45F5 0.45 0.45 0.45 0.45 0.45 0.45F6 0.45 0.45 0.45 0.45 0.45 0.45

Table 5 Feature extraction (energy) with Bθ = Sθ = 30o (Singh index = 5)

0o 30o 60o 90o 120o 150o

F0 0.51 0.48 0.51 0.49 0.51 0.48F1 0.31 0.01 0.01 0.29 0.01 0.01F2 0.02 0.01 0.01 0.02 0.01 0.01F3 0.06 0.05 0.05 0.05 0.04 0.04F4 0.52 0.53 0.53 0.47 0.52 0.52F5 0.52 0.52 0.52 0.52 0.52 0.52F6 0.52 0.52 0.52 0.52 0.52 0.52

Table 6 Feature extraction (energy) with Bθ = Sθ = 45o (Singh index = 5)

0o 45o 90o 135o 180o 225o

F0 0.51 0.51 0.49 0.51 0.51 0.51F1 0.31 0.08 0.29 0.07 0.31 0.08F2 0.02 0.00 0.02 0.00 0.02 0.00F3 0.06 0.07 0.05 0.07 0.06 0.07F4 0.52 0.53 0.47 0.52 0.52 0.53F5 0.52 0.52 0.52 0.52 0.52 0.52F6 0.52 0.52 0.52 0.52 0.52 0.52

From Table 1 to 6, it is clear that for trabecular pattern at proximal femur, features extraction have a consistent result for Bθ = Sθ = 30o and Bθ = Sθ = 45o at center frequency of F5 (√2/25 cpi) and F6 (√2/26 cpi). Therefore for the rest of experiment we use Gabon filter with Bθ = Sθ = 30o, normalized center frequencies

of and with 0o, 30o, 60o, 90o, 120o, 150o

orientations. After the extracted features of trabecular pattern of all sample images have been obtained second features extraction is performed using energy function at norm-l1 defined as

(6)

where x(m, n) is a matrix which the elements are extracted features with Gabor filter with center

frequencies of and and 0o, 30o, 60o, 90o, 120o,

150o orientations. The extracted features in the form of energy from 55 radiographs of proximal femur are listed in Table 7 and also showed in graphical form in Figure 8.

Table 7 Extracted features from 55 radiographs

File Number

Image Files Energy Singh

index1 F3-1.tif 0.34 32 F3-2.tif 0.40 33 F3-3.tif 0.38 34 F3-4.tif 0.36 35 F3-5.tif 0.34 3

6 F3-6.tif 0.37 37 F3-7.tif 0.39 38 F3-8.tif 0.38 39 F3-9.tif 0.37 3

10 F3-10.tif 0.39 311 F3-11.tif 0.38 3

Table 7 Extracted features from 55 radiographs (Cont’d.)

File Number

Image Files Energy Singh

index12 F3-12.tif 0.35 313 F3-13.tif 0.37 314 F3-14.tif 0.38 315 F3-15.tif 0.30 316 F4-1.tif 0.44 417 F4-2.tif 0.46 418 F4-3.tif 0.45 419 F4-4.tif 0.42 420 F4-5.tif 0.45 421 F4-6.tif 0.47 422 F4-7.tif 0.47 423 F4-8.tif 0.47 424 F4-9.tif 0.46 425 F4-10.tif 0.46 426 F4-11.tif 0.49 427 F4-12.tif 0.48 428 F4-13.tif 0.45 429 F4-14.tif 0.41 430 F4-15.tif 0.40 431 F4-16.tif 0.48 432 F5-1.tif 0.57 533 F5-2.tif 0.52 534 F5-20.tif 0.52 535 F5-3.tif 0.53 536 F5-4.tif 0.49 537 F5-5.tif 0.51 538 F5-6.tif 0.51 539 F5-7.tif 0.52 540 F5-8.tif 0.48 541 F5-9.tif 0.58 542 F5-10.tif 0.50 543 F5-11.tif 0.53 544 F5-12.tif 0.52 545 F5-13.tif 0.52 546 F5-14.tif 0.46 547 F5-15.tif 0.51 548 F5-16.tif 0.57 549 F5-17.tif 0.51 550 F5-18.tif 0.55 551 F5-19.tif 0.53 5

52 F6-1.tif 0.67 653 F6-2.tif 0.67 654 F6-3.tif 0.62 655 F6-4.tif 0.62 6

The energy calculated from particular trabecular pattern of grade 6 samples appears to have the highest value and the energy from grade 3 samples has the lowest value. In between, almost all samples of grade 5 and 4 have energies that agreed with their corresponding Singh Indexes. The result of energy computation for 55 radiographs samples in the graphical form is shown in Figure 7.

Fig. 8 Graphics of extracted features (energy) of 55 radiographs

7 ConclusionWe have introduced a machine vision system for osteoporosis assessment. Extracted features from trabecular pattern that are recorded in proximal femur radiographs by Gabor filter match with their predetermined Singh index. The extracted features of trabecular pattern could represent the quality or structure of the bone. To achieve better result in future work, the acquisition of radiographs should be standardized in terms of distance, energy excited and the position of patients.

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