2023年12月1日发(作者：海尔笔记本官网)

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INTEGRATING EDGE DETECTION AND

THRESHOLDING APPROACHES TO SEGMENTING

FEMORA AND PATELLAE

FROM MAGNETIC RESONANCE IMAGES

12

JY

IANNHUEEIUNGHUNG

-SL, -NC

1

Department of Information and Learning Technology, National University of Tainan,

Tainan, Taiwan

2

Department of Electrical Engineering, Da-Yeh University, Da-Tusen, Taiwan

ABSTRACT

Anterior knee pain (AKP) is a common pathological condition. The most obvious problem

causing knee pain is the abnormal patellar tracking mechanism. For computerized knee joint

analysis, how to successfully segment the knee bones is an import issue. This paper presents a simple

while effective algorithm for fully automatic femur and patella segmentation for magnetic resonance

(MR) knee images through integrating edge detection and thresholding approaches. Based on

consideration of computational complexity and accuracy, we develop a compound approach to

segment the MR knee images. The moment preserving thresholding is first utilized to gather the bone-

outline information employed to estimate the region of interest (ROI). An ROI based wavelet

enhancement is proposed to restrict the contrast improvement only around the bone edges. The

restriction makes both the adhesion separation of bone and surrounding tissues and the bone contour

conservation become possible and avoid harsh thresholding resulting from the global based wavelet

enhancement. Cooperating with the morphology operation, stable initial guess of the bone regions

can be achieved. To overwhelm the main drawback of the existing edge based segmentation methods,

i.e. the necessity of complicated post-processing, a new approach - FLoG is proposed to provide a

feasible solution. It converts the edge detection results using LoG into a region-based format through

the flow fill operation. The developed onion-growing algorithm can properly combine the initial

guess of bone regions with the FLoG outputs in an efficient way. The experimental study shows our

method is superior to the conventional ones in meeting the requirement of physicians. This is because

our method can perform well in dealing with the tougher conditions, i.e. the partial volume and the

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patella, walk down stairs or keep the knee bent for a

long period. The generic AKP syndrome can be further

categorized to different conditions [4] like patella

dislocation, chondromalacia patellae [5-7] and retro-

patellar pain. The reason for occurrence of AKP is still

not fully understood. However, the most obvious

problem is the abnormal patellar tracking mechanism.

The abnormality may result from either muscular or

structural imbalance. Patella movement is dominated

by the quadriceps. Once a muscle imbalance occurs,

the patella tends to stray from its normal path and

results in pain. As to structural imbalance, the mal-

alignment of the patella is the major cause. Both

muscular and structural imbalance will induce wear

and tear to the cartilage and bring about pain.

Traditional examining approaches to patellar

tracking are stationary based. During the overall

examination process patients

legs are fixed. Because

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and 6 demonstrate the experimental results and draw a

conclusion, respectively.

2. THE INITIAL SEGMENTATION

Automatic segmentation of medical images serves

as the key step in applications such as computer aided

diagnosis and qualitative studies. A wide variety of

image segmentation algorithms have been proposed in

the literature. However, a popular technique in image

segmentation is thresholding, which is computationally

simpler than other existing algorithms, e.g. boundary

detection, region-based techniques or active contour

dependent methods. The frequently used thresholding

algorithms are Otsu

s between class variance method

[12], moment preserving method [13] and entropy

method [14]. Depending on applications, either bi-level

or multi-level thresholding is applied. Due to the

partial volume effect, multi-level thresholding will

cause the bones to be segmented as fragments. This

will increase the following process complexity thus bi-

level thresholding was adopted. To select the suitable

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approach, the segmented bones should conserve fine

parts as far as possible. That is, we want the adhesion

of bone and surrounding tissues to be as slight as

possible after thresholding. This goal can be achieved

by the following wavelet based enhancement.

Wavelet transforms (WT) [21-22] based image

analysis is a valuable tool for image enhancement since

it can be used to highlight scale-specific or subband-

specific image features. In addition, these features

remain localized in space, thus many spatial domain

image enhancement techniques can be adapted for the

WTdomain. The WTdomain contrast enhancement

algorithms can be divided into manipulating the detail

coefficient sets or the approximation coefficient sets

that result from WT decomposition. The latter

manipulation mainly applies global histogram

equalization to the approximation coefficient sets and

then adds back the image's small-scale high frequency

features. Resulting from the phenomenon that the

background gray-level concentrates in low intensity,

this approach will degrade the image contrast. In our

case, we want to enhance the intensity difference

around the junctions of the bone and soft tissue. To

attain this goal, the former approach is more suitable.

The image I(x,y) is decomposed into the WT

domain by using the one-dimensional decomposition

filters g() (high pass filter) and h()(low pass filter)

..

applied separately to the rows and/or columns of I(x,y).

The decomposition of an arbitrary image

approximation and details at scale j, i.e. A

j

(x,y) and

(x,y) are given by:

bones. This will lead the subsequent thresholding

operation to generate harsh segmentation. Fig. 4

demonstrates the harsh segmentation resulting from

global enhancement. To resolve the problem, we

restrict the edge contrast enhancement around the bone

and soft tissue junctions. Recall that we have obtained

the rough segmentation, i.e. TI, after the first time

thresholding. Hence, we can approximately estimate

the bone and soft tissue junction zone (BJZ) from TI.

First, the erosion operation with a larger structure

element SE2, as shown in Fig. 5(a), is applied to TI.

The larger structure element is adopted to ensure the

severance for the bone and soft tissue adhesion. Then,

the labeling operation is followed. Usually, the femur

and the patella are a first and a second in size along the

horizontally middle line. We can identify them easily

by using this property. However, for some abnormal

imaging conditions, the muscle intensity is higher than

the bone intensity. In such case, the muscle area will be

the biggest. Therefore, we also examine if the biggest

region is the most outer tissue to exclude this situation.

Next, the bones are set to one and the others are set to

zero. After identification, the dilation operation with

the structure element SE2is applied to the two pieces

of bone. The dilated result is denoted as DBI(dilated

bone image). To estimate the BJZ, the following

operations are performed.

For dyadic decomposition, the subscript jdenotes

the scale 2

j

. The coefficient sets are generated by down

sampling by a factor of two after each convolution.

The denotes the detailed coefficient set with

orientation

determined by the direction (horizontal,, w, w)

vertical or diagonal) in which the high-pass filter isare (w/2, w/2, w/2), accordingly. The wis

employed. Here, the biorthogonal spline wavelets arethe initial magnification factor corresponding to the

adopted. We magnify the detail coefficients prior to

reconstruction such that promising edge contrastthe magnification factors increase by the scale

enhancement is achieved. parameter factor, i.e. (w

The magnification factors can be either scale-

irrelevancy or scale-relevancy. The enhancement

region can be either local or global. Global

enhancement does not only enhance the bone and soft

tissue junctions but also enhance the interior texture of

where SE3and SE4are structure elements shown

in Fig. 5(b) and (c),

denotes the erosion operation,

denotes the exclusive-OR operation, and denotes

the dilation operation. The estimated BJZof Fig. 6(a)

is shown in Fig. 6(b). The superimposition

consequence of the original image and the BJZis

demonstrated in Fig. 6(c). The result demonstrates that

the BJZ estimation approach can successfully restrict

the edge contrast enhancement around the bone and

soft tissue junctions.

To seek proper magnification factors many

magnifying strategies, including the scale-decrease, the

scale-increase and the scale-irrelevancy, are examined.

The test results are summarized in Table I. For the

scale-decrease approach, the magnification factors

decrease by the scale parameter factor, i.e. (w

12 3

012

first scale. Similarly, for the scale-increase approach,

12 3

, w, w) are (2w, 2w, 2

012

w), accordingly. As for the scale-irrelevancy

approach, the triple of the magnification factors (w,

1

w, w) is (w, w, w), individually. From the

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experimental study, we conclude that the thresholding

outcome of the ROI based approach is not very

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Fig. 3. (a) A thresholded result with severe bone and

soft tissue adhesion, (b) the initial guess of bone

regions using a 7x7 SE, and (c) the initial guess of

bone regions using a 9x9 SE.

Fig. 4. The thresholded result using global based

wavelet enhancement.

sensitive to the magnification factors. And, for the

bone and soft tissue severance, the scale-decrease

approach is superior to others. Among those test triples

of factors, the triple (1, 0.5, 0.25) produces the most

pleasing output and is adopted in our algorithm. The

thresholded image after the wavelet enhancement is

denoted as WETI. Usually, the WETIis still over

detected and may possess undesired adhesion but the

adhesive degree becomes insignificant. The

improvement in the adhesive degree enables the

succeeding erosion operation to conserve the bone

outlines as well as to ensure the severance for the bone

and soft tissue adhesion. The erosion operation with a

smaller structure element SE4is applied to the WETI.

Then, the labeling procedure is followed. According to

the property that the femur and the patella are a first

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the second derivative. The latter technique is optimal

for step edges corrupted by white noise. The optimality

of the detector is related to three detection,

localization and single response. Compared to the

Canny detector, the LoGis simpler and more attractive.

This is because the zero-crossings produced by the

LoGtend to create closed loops of edges nicknamed

the

plate of spaghetti' effect. This effect has been

seen as a drawback in many applications. However,

this property lends itself to the conversion of the

detected edges from the pixel-based mode to the

region-based style and makes the extraction of object

contours easier. Thus, the LoGis adopted at this stage.

Selecting a proper standard deviation is an important

stage for the utilization of the LoG. The parameter will

affect the noise sensitivity and the edge locating of the

LoGoperation. The empirical value,

= 1.8, which is

the compromising result under the consideration of

both factors.

To simplify the description of the subsequent

algorithm, Fig. 7(a) is selected for an example. First,

the flow fill operation is exerted to convert the edge

image into region-based style. Observing the zero-

crossing image (i.e. Fig. 7(b)), we can find that the

starting point selection of the flow fill operation is not

trivial. An improper starting point will lead to

undesired filling results. The proper starting positions

are the vicinage of the bones. To estimate the most

appropriate starting positions we trace the DBI border

once. On the traced point, its neighborhood

perpendicular to the tracing direction is examined. The

examination window, as shown in Fig. 8, is planted on

the corresponding locations in both the zero-crossing

map and the original image. If only one edge pixel

appears in the window, the gray intensity of the point

next to the edge pixel toward the outer direction is

recorded. After tracing the DBIborder once, the

recorded point with the lowest intensity is selected as

the starting position for the flow filling. And, the filled

image Fig. 7(c) is denoted as FI. We let IFIrepresent

the inverse of the FI. Subsequently, the IFIANDs the

original image I to set the filled area to zero intensity

level. The result as shown in Fig. 7(d) is called the

masked image. In the masked image, the bones are

surrounded by a zero-intensity-zone. Combining this

property with the bone position information acquired

in the EBI, the femur and the patella can be identified

easily by filling from the masked image. We name the

identified bones the IBR(initial bone regions). We find

that the extracted bones are very accurate except some

breaches resulting from the gray-level inhomogeneity

in the femur and the patella.

Fig. 7. (a) The test image, (b) its zero-crossing map,

(c) the filled image, (d) the masked image after

thresholding, and (e) the superimposition result of

the detected bone contours and (a).

4. THE ONION-GROWING

ALGORITHM

To patch these breaches, we propose an onion-

growing algorithm. We know that the bones in the EBI

are thinner than the actual ones while conserve outlines

of the actual bones. Based on this property, we can

thicken the EBI bones iteratively pixel by pixel through

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one by and step 2 is repeated. Let OPN(i)= OPN(i)-

OPN(i-1). If the OPN(i)is larger than the threshold

value th, the thickening procedure is terminated.

Otherwise, the index iincreases one and step 2 is

repeated.

Step 4.The estimated bone regions BRis

achieved by

where

means the OR operation.

The underlying principle of step 3 is that if the

thickened EBIalmost coincides with the IBRCthe

OPNwill increase significantly. Hence, we can

determine the iteration number through measuring the

OPN.

Fig. 8. A diagram used to explain how to select the

proper starting point for flow filling operation.

5. THE EXPERIMENTAL RESULTS

We gathered forty patientsMR knee image sets.

Each set comprises six knee images corresponding to

six individual bending angles. Segmenting these

images with our program and comparing the outcomes

with those obtained manually, we got the average error

ratio for each patient shown in Fig. 9. Let FPijand

FMij represent the femur region in the jth image of the

patient isegmented with our program and the manual

operation, respectively. Similarly, PPijand PMij

denote the patella region in the jth image of the patient

isegmented with our program and the manual

operation, respectively. The average error ratio of the

femur segmentation for the patient i, i.e. EFi, can be

calculated by

Error ration(%)

(a)

Error ration(%)

(b)

Fig. 9 (a) The average error ratio of the femur

segmentation for each patient. (b) The average

error ratio of the patella segmentation for each

patient.

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where

and denote binary exclusive-OR and

AND operations, respectively. The average error ratio

of the patella segmentation for the patient i, i.e. EPi,

can be calculated by

likewise. Fig. 9(a) shows that the average error

ratios of the femur segmentation for the all gathered

patients are less than one percentage. The worst case

happens when significant edge occurs between bone

and partial volume portion. This situation is

demonstrated in Fig. 10. Although this case is seldom

encountered, we still try to solve the problem in our

future research. The average error ratios of the patella

segmentation for the all gathered patients are shown in

Fig. 9(b). We can find that the error ratio of patella is

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Table 1. The summarized thresholding results adopting different magnification strategies. The members of

each triple correspond to (w

1 2 3

, w, w).

more significant than that of femur. This is because the

patella is far less than the femur in size. To show the

effectiveness of our method, two other samples were

also examined. Fig. 11(a) and 12(a) are the two tested

knee images. The desired bones contours for the

physician are shown in Fig. 11(b) and 12(b). Fig. 11(c)

and 12(c) are the results obtained from Kitney's

approach. We observed that Kitney'sapproach tends to

under- and over-segmentation for partial volume cases

and soft tissue adhesion cases, respectively. This is

because their segmentation scheme mainly relies on

edge magnitude, which is significant for adhesion

tissue while petty for partial volume portion, coming

from the Sobel operation. The segmentation results

produced from deformable model [19], with initial

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Fig. 10. This example is used to illustrate the

limitation of the proposed method. (a) An image

with significant edge between bone and partial

volume portion, which is indicated by an arrow

sign. (b) The extracted boundaries by using the

proposed method.

Fig. 12 (a) The test image. (b) The desired contours

of the femur and the patella depicted by the

physician. (c) The extracted boundaries by using

Kitney

s approach. (d) The extracted boundaries

by using the deformable model. (e) The extracted

boundaries by using the proposed method.

6. CONCLUDING REMARKS

To minimize subjectivity and time cost as well as

to maximize validity and reproducibility, a fully

automatic femur and patella segmentation approach is

proposed. Under the stable and efficient consideration,

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