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BAYESIAN IMAGING CONCEPTS FOR SMART FRACTURE
DETECTION IN X-RAY IMAGES
Dr. R.Harikumar1, P.S.Karthik 2, K.S.Prabakaran3, S.Sivaprakash4
1Professor, Bannari Amman Institute of Technology Sathyamangalam
2,3,4U.G students, ECE, Bannari Amman Institute of Technology, Sathyamangalam
Abstract— X-ray imaging is a traditional method for detecting fracture for ages. This project paves way for enhancement rather than replacement of the existing technology. It is a step towards thinking beyond digitization of X-ray. This main objective is to provide a better enhanced methodology for reconstructing X-ray images. This is done by incorporating the Bayesian concept of image processing into it. The X-ray is obtained as a running video, decoded, digitized and fed into the processing element. The Very Long Instruction Word (VLIW) architecture supporting high speed DSP core TMS320C6455 is used to perform the image enhancement algorithm. The processed image with higher degree of clarity is thus obtained with a good PSNR value. This reconstructed image can then be directed to the display device (LCD Monitor), through a LCD display driver interfaced with the processor. This device also has the potential to take the form of a portable handheld device with certain transformations made to it.
Keywords— Bayesian Concept, Enhanced methodology, PSNR value, VLIW architecture.
I. INTRODUCTION
A bone fracture is a medical condition in which there is a break in the continuity of the bone as a result of high force impact or stress, leading to heavy pain and bulging of body. Bone fracture can also occur as a result of certain medical conditions that weaken the bones, certain types of cancer. The fracture complexity may vary from minor cracks to literal breaking of the bone.
Open bone fractures are identified by bare eyes, because as the name suggests they make an opening in the body where they happen. The ideal way to diagnose the closed bone fracture is by taking X-ray photograph (Medical radiography) in the suspected area of the bone, which is then examined to see if there is any hairline fracture in the bone. The X-ray photography usually shows the complete skeleton of the part under consideration.
A. Applications of X-rays – Review
X-radiation (composed of X-rays) is a form of electromagnetic radiation. X-rays have a wavelength in the range of 10 to 0.01 nanometres, corresponding to frequencies in the range 30 Petahertz to 30 Exahertz. An important feature of the X-ray is its penetration power. X-rays can penetrate solid objects, and their largest use is to take images of the inside of objects in diagnostic radiography. The fact that the X-rays are able to pass through the flesh of the human body and are reflected by the bones make them eligible for use in the radiography.
Radiographs are produced by the transmission of X-rays through a patient to a capture device then conversion into an image for diagnosis. The original and still common imaging produces silver impregnated films. In Film - Screen radiography an X-ray tube generates a beam of X-rays which is aimed at the patient. The X-rays which pass through the patient are filtered to reduce scatter and noise and then strike an undeveloped film, held tight to a screen of light emitting phosphors in a light-tight cassette. The film is then developed chemically and an image appears on the film. The image obtained by this method shows the complete structure of the bone and the remaining part being black. Any crack in the bone or displacement at joints can be identified from it. But in case of minor cracks in the bone these films, sometimes, may prove inefficient, which is not acceptable. This has to be eliminated. One way is to produce an image of with more clarity without losing any vital information in the image. This can be done processing the image using a better efficient image reconstruction algorithm. In this project the Bayesian Imaging concepts was adapted for the enhancement of the original image and then the reconstructed image is displayed on the screen.
B. Statement of the problem
As stated above, Radiography is the most common method used today for the diagnosis of fractures in the human body. But the disadvantage of this method is it may sometimes become uncertain in the case of hair line cracks. These small cracks in the bone go unnoticed in the X-ray Photography due to the noise disturbances and the quality of the image construction. Eventually the potential of the cracks develop and may result in a compound fracture.
C. Organization of the Report
The Bayesian approach provides the means to incorporate prior knowledge in data analysis. Bayesian analysis revolves around the posterior probability, which summarizes the degree of one’s certainty concerning a given situation. Bayes’ law states that the posterior probability is proportional to the product of the likelihood and the prior probability. The likelihood encompasses the information contained in the new data. The prior expresses the degree of certainty concerning the situation before the data are taken. Although the posterior probability completely describes the state of certainty about any possible image, only a single image is required as the ‘result’ or reconstruction. A typical choice is that image that maximizes the posterior probability, which is called the maximum a posteriori (MAP) estimate. In situations where only very limited data are available, the data alone may not be sufficient to specify a unique solution to the problem. The prior introduced with the Bayesian method can help guide the result towards a preferred solution. As the MAP solution differs from the Maximum Likelihood (ML) solution solely because of the prior, choosing the prior is one of the most critical aspects of Bayesian analysis.
II. Methodology
A. Block diagram
Figure 1: Block diagram of the Implementation Process
In order to estimate the efficiency of the algorithm, it is essential to see the effect of it in an existing X-ray image. Therefore an X-ray photograph of a fracture patient is considered. The data from the photograph is converted to electrical terms by means of capturing the photograph through a Camera with proper setup. The data, which is in the form of video (NTSC/PAL format), is then given as input to a video decoder card, which converts them into bits for further processing. The DSP Starter Kit TMDSMDSK6455, connected to the video decoder, acquires the data which comes from it. The Digital Signal Processor TMS320C6455 then implements the BAYESIAN IMAGE RECONSTRUCTION algorithm on the received data. Thus the image is enhanced. The data after reconstruction is then send to the LCD Display driver which is connected between the processor and the output display device, LCD Monitor. The LCD driver converts the data in to a form which is acceptable by display device. Finally the enhance image is displayed as video in the LCD display Monitor.
B. Proposed Solution
The one solution for the problem cited above is to enhance the X-ray image obtained from the photograph using a specialized image processing algorithm. One such algorithm is the BAYESIAN IMAGE RECONSTRUCTION algorithm. The use of Bayesian concepts provides more clarity to the image thereby revealing the minute information present in the image, very clearly. Then by displaying it in a display screen would definitely help the doctors to identify the hair line cracks if any during diagnosis and therefore save the patients from the future problems.
C. Bayesian Algorithm
The first aspect of Bayesian analysis involves the interpretation of Equation,
Suppose we wish to improve our knowledge concerning a parameter x, our present state of certainty is characterized by the probability density function p(x). We perform an experiment and take some data d. By decomposing the joint probability as in Eq. (1) both ways, and substituting d for y, we obtain Bayes’ law:
We call p(x|d) the posterior probability density function, because it effectively follows (temporally or logically) the experiment. The probability p(x) is called the prior because it represents the state of knowledge before the experiment. The quantity p(d|x) is the likelihood, which expresses the probability of the data d given any particular x.
The likelihood is usually derived from a model for predicting the data, given x, as well as a probabilistic model for the noise. Bayes’ law provides the means for updating our knowledge, expressed in terms of a probability density function, in light of some new information, similarly expressed.
The term in the denominator p(d) may be considered necessary only for normalization purposes. In one interpretation of Bayes’ law, the prior p(x) represents knowledge acquired in a previous experiment. In other words, it might be the posterior probability of the previous experiment. In this case, Bayes’ law can be interpreted as the proper way to calculate the sum total of all the available experimental information. The prior might be viewed as a means to restrict x so that the posterior provides more information about x than the likelihood. In this situation, the prior is not necessarily restricted to what is known before the experiment. Indeed, many different priors might be employed in the Bayesian analysis to investigate the range of possible outcomes. The proper choice for the prior clearly depends on the domain of the problem.
D. Choice of Estimator
The second aspect of Bayesian analysis deals with the use of the posterior probability. While the posterior probability density function p(x|d) fully expresses what we know about x, it may embody more information than is required. When attempting to summarize the results of an analysis, it may be necessary to represent p(x|d) in more concise terms. For example, it might be desirable to quote a single value for x, which we call the estimate, designated as ˆx. Alternatively, it might be that a decision is required, perhaps in the form of a binary decision: yes, a certain object is present, or no, it is not. In this interpretation process some information concerning p(x|d) is lost. The crucial point is that through cost analysis the Bayesian approach provides an optimal way to interpret the posterior probability. To achieve optimality, it is necessary to consider the costs (or risks) associated with making various kinds of errors in the interpretation process. The assignment of the proper cost function is typically considered to be a part of specifying the problem.
The choice of an estimation method to select the single value that is most representative of what we know about x clearly depends on, how one assigns significance to making errors of various magnitudes.
As the posterior probability can be used to calculate the expected error, the choice of an estimation method can be based on the posterior probability density function itself. A standard measure of the accuracy of a result is the variance (or mean square error). Given the posterior probability density function p(x|d), the expected variance for an estimate ˆx is
|x − ˆx|2 dx (3)
It is fairly easy to show that the estimator that minimizes (3) is the mean of the posterior probability density function
ˆx = (x|d) dx (4)
When any answer other than the correct one incurs the same increased cost, the obvious estimate is the value of x at the maximum of the posterior probability density function:
ˆx = argmax p(x|d) (5)
This choice is the well-known maximum a posteriori (MAP) estimator. For unimodal symmetric density functions, which include Gaussians, all the above estimators yield the same result. However, In case of the posterior probability being asymmetric or has multiple peaks, then these various estimators can yield quite different results, so the choice of an appropriate estimator becomes an issue. It is important to remember that each estimator minimizes a specific cost function.
III. Hardware Implementation
A. Choice of Hardware
The complete hardware used in the project may be grouped into three different units.
Pre-processing Unit
The pre-processing unit is used to convert the input acquired into a form the processor can accept. The hardware used in this unit is a Video decoder (VM3224K2), which is used to decode the analog video input (PAL/ NTSC) into digital format. The synchronization pulses, between each frame are detected. These pulses, void of image data, are eliminated and only the data corresponding to the image is taken for algorithm implementation.
The important features of the decoder card are given below:
· Input: NTSC/PAL, 30/25 fps
· Output: RGB565
· Resolution: 320x240 16bit/pixel
Processing Unit
The main function of this unit is implementation of the algorithm and uses the TMDSMDSK6455 DSK for the same that contains the TMS320C6455 Digital Signal Processor as its core. The algorithm to be implemented is fed into the processor using the IDE - Code Composer Studio. Then digital input is received from the decoder through one of the extension slots provided in the DSK. The input stored in the memory is then retrieved and processed using the Bayesian Algorithm.
After processing, the new data is then stored and also directed to the output device for display. The advantage of using this starter kit for the processing is that, it is built specially for MEDICAL IMAGING. The DSK features the TMS320C6455 DSP, a 1.2 GHz device delivering up to 8000 million instructions per second (MIPS) and is designed for products that require the highest performing DSPs. The C6455™ is based on the high performing TMS320C64x+™ DSP platform designed to needs of high-performing memory intensive applications such as networking, video, imaging, and most multichannel systems. The other hardware features which make them most suitable for the implementation of this algorithm are,
· Embedded XDS510-class JTAG support via USB
· 128MB Memory and 8MB Flash
· Expansion port connector for plug-in modules
· EMIF (32bit data) & McBSP0 to Connector 1
Post- Processing Unit
The post processing unit is output display device and a display driver, for the display device to interface with the processor. The output display device is an LCD Monitor which is used to display the reconstructed image. The display driver is an LCD controller, which drives the monitor with the data that comes from the processor. The LCD controller converts the processed data, which comes from the processor into a format which the monitor can read.