Assessment of Performance Improvement in Content-based Medical Image Retrieval Schemes Using Fractal Dimension

Rationale and Objectives

The aim of this study was to investigate whether using a fractal dimension as an objective index (quantitative measure) to assess and control the “visual” or “texture” similarity of reference-image regions selected by a content-based image retrieval (CBIR) scheme would (or would not) affect the performance of the scheme in classification between image regions depicting suspicious breast masses.

Materials and Methods

An image data set depicting 1500 verified mass regions and 1500 false-positive mass regions was used. Fourteen morphologic and intensity distribution features and a fractal dimension were computed. A CBIR scheme using a k -nearest neighbor classifier was applied, and two experiments were conducted. In the first experiment, the CBIR scheme was evaluated using all 15 features. In the second experiment, the fractal dimension was used as a prescreening feature to guide the CBIR scheme to search for the most similar reference images that had similar measures in the fractal dimension.

Results

The CBIR scheme achieved classification performance with areas under the receiver-operating characteristic curve of 0.857 (95% confidence interval [CI], 0.844–0.870) using 14 features and 0.866 (95% CI, 0.853–0.879) after adding the fractal dimension ( P = .005 for both results). After using the fractal dimension as a prescreening feature, the CBIR scheme achieved an area under the receiver-operating characteristic curve of 0.851 (95% CI, 0.837–0.864), without a significant difference from the previous result using the original 14 features ( P = .120). The difference of fractal dimension values between the selected similar reference images was reduced by 56.7%, indicating improvement in image texture similarity. In addition, more than half of references were discarded early, without similarity comparisons, indicating improvement in searching efficiency.

Conclusions

This study demonstrated the feasibility of applying a fractal dimension as an objective (quantitative) and efficient search index to assess and maintain the texture similarity of reference mass regions selected by a CBIR scheme without reducing the scheme’s performance in classifying suspicious breast masses.

Content-based image retrieval (CBIR) schemes have been developed to search for images similar to a queried image from large reference-image databases on the basis of features or image content inherently contained within the images . In particular, the CBIR method has been proposed to overcome the difficulties encountered in textual annotation or description by manual methods for large image databases . Although the use of purely visual image querying is unlikely to be able to completely replace text-based searching methods, CBIR has the potential to be a very useful complement to text-based searching methods because of unique image characteristics . In the field of computer vision, CBIR has been one of the most active research areas over the past 30 years .

Currently, with the advances in digital technologies applied to medical imaging, a large number of diverse radiologic and pathologic images in digital format are rapidly produced in hospitals and medical centers using sophisticated image acquisition devices and digital scanners. These digital images have been routinely used for the purposes of diagnosis and therapy. The management of and access to these large image repositories has become increasingly complex and challenging . In reading and interpreting medical images in daily clinical practice, observers (ie, radiologists and pathologists) are often faced with new unknown and suspicious lesions, requiring them to search for and make comparisons to similar cases with previously verified results in their decision making in detection and diagnosis . This is a difficult and very time consuming task because of the rapid increase in the sizes of medical imaging databases. Therefore, developing and applying CBIR schemes to more effectively organize and retrieve images has attracted wide research interest in medical imaging and informatics . In particular, a number of studies have recently been conducted on how to develop and optimize CBIR schemes to search for similar breast lesions (including masses and microcalcification clusters) .

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Materials and methods

Reference-image Database

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Fractal Dimension

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P(u,v)=∣∣F(u,v)2∣∣=R(u,v)2+I(u,v)2, P

(

u

,

v

)

=

|

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(

u

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=

R

(

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2

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where u and v represent the horizontal and vertical components of frequencies, respectively, and R ( u , v ) and I ( u , v ) are the real and imaginary parts of the Fourier transform F ( u , v ), respectively. The power spectrum is displaced in polar form and shifted to locate zero frequency at the center. The scheme calculates log[ f ( u , v )], where f(u,v)=u2+v2−−−−−−√ f

(

u

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=

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2

+

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2 , and average log[ P ( u , v )] in the condition of f(u,v)≤u2+v2−−−−−−√ f

(

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≤

u

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+

v

2 . Each set of u and v is defined by every 0.1 of log[ f ( u , v )] ( Fig 1 a). The slope of the curve on average log[ P ( u , v )] versus log[ f ( u , v )] is calculated by least-squares fitting ( Fig 1 b). Finally, the fractal dimension is calculated as

fractaldimension=(7−slope)/2. fractal

dimension

=

(

7

−

slope

)

/

2.

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CBIR Scheme Using a k -Nearest Neighbor Classifier

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d(yT,xi)=∑FNr=1[fr(yT)−fr(xi)]2−−−−−−−−−−−−−−−−−−−√. d

(

y

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N

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A smaller distance indicates a higher degree of “similarity” between two compared regions. The k NN classifier then computes a detection score to indicate the likelihood of being a true mass to the queried region:

PTP=∑Ni=1wTPi∑Ni=1wTPi+∑Mj=1wFPj,N+M=K, P

TP

=

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where w i = 1/[ d ( y T , x i )] 2 (a distance weight), and wTPi w

i

TP and wFPj w

j

FP are the distance weights for the true-positive ( i ) and false-positive ( j ) mass regions, respectively. N is the number of verified true-positive mass regions, and M is the number of CAD-cued false-positive regions.

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Performance Evaluation

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Results

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Table 1

Performance of the Content-Based Image Retrieval Scheme and the Average Number of Early Discarded (Removed) Reference ROIs as a Function of the Comparison Threshold of the Fractal Dimension

α (Half of Difference Between Two Fractal Dimensions)A z 95% CI Average Number of Removed Reference ROIs 0.06 0.843 0.844–0.870 2140 0.07 0.843 0.829–0.857 1967 0.08 0.845 0.931–0.859 1835 0.09 0.850 0.836–0.862 1709 0.10 0.851 0.837–0.864 1588 0.20 0.853 0.839–0.866 695 0.30 0.853 0.839–0.865 272

A z , area under the receiver-operating characteristic curve; CI, confidence interval; ROI, region of interest.

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Discussion

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