changes [4]. Improvements in fundus imaging with trans- lation from the film based photography camera to use of. CCD and CMOS based electronic sensors; ...
2013 IEEE 10th International Symposium on Biomedical Imaging: From Nano to Macro San Francisco, CA, USA, April 7-11, 2013
DETECTION OF RETINAL VESSELS IN FUNDUS IMAGES THROUGH TRANSFER LEARNING OF TISSUE SPECIFIC PHOTON INTERACTION STATISTICAL PHYSICS D. Sheet1 , S.P.K. Karri1 , S. Conjeti1 , S. Ghosh3 , J. Chatterjee1 and A.K. Ray2 1
School of Medical Science and Technology, Indian Institute of Technology Kharagpur, India Electronics and Electrical Comm. Engg., Indian Institute of Technology Kharagpur, India 3 North Bengal Medical College and Hospital, Darjeeling, India
2
ABSTRACT Loss of visual acuity on account of retina-related vision impairment can be partly prevented through periodic screening with fundus color imaging. Largescale screening is currently challenged by inability to exhaustively detect fine blood vessels crucial to disease diagnosis. In this work we present a framework for reliable blood vessel detection in fundus color imaging through inductive transfer learning of photon-tissue interaction statistical physics. The source task estimates photon-tissue interaction as a spatially localized Poisson process of photons sensed by the RGB sensor. The target task identifies vascular and non-vascular tissues using knowledge transferred from source task. The source and target domains are retinal images obtained using a color fundus camera with white-light illumination. In experimental evaluation with the DRIVE database, we achieve the objective of vessel detection with max. avg. accuracy of 0.9766 and kappa of 0.8213. Index Terms— Vessel detection, retinal imaging, machine learning, inductive transfer, statistical physics, random forests. 1. INTRODUCTION Loss of visual acuity leading to blindness on account of degeneration of the retina can be prevented through regular screening practices [1, 2]. Fundus imaging till date is the most widely used modality for population-based large scale detection of diabetic retinopathy, glucoma, age-related macular degeneration [3], hypertension and stroke induced changes [4]. Improvements in fundus imaging with translation from the film based photography camera to use of CCD and CMOS based electronic sensors; as well as red free imaging, stereo photography, hyperspectral imaging, angiography, etc. [5] have reduced variability in clinical reporting of pathologies. Significantly related contributions have also been on account of retinal image analysis [5, 6]. Since fundus imaging is predominantly used for first level of abnormality screening, research focus includes: (i) localization and segmentation of retinal structures (vessels, fovea, optic disc), (ii)
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(a) Fundus color image
(b) Ground truth
(c) Detected vessels
Fig. 1. Illustration of retinal vessel detection in color fundus image using our proposed method. Sample #11 in [7].
segmentation of abnormalities, and (iii) quality quantification of images acquired to assess reporting fitness [5]. Related Work: The process of reporting during retinal screening is systematic and thus computer assisted diagnosis systems developed specifically according to the clinical workflow have improved quality of healthcare delivery [5]. These approaches include, assessing quality of the image [8]; detecting blood vessels [7], their branching pattern, diameter and tree analysis [3, 4, 9, 10]; followed by reporting of lesions and their location with respect to the vessels [4, 10]. An important challenge here is robust and exhaustive detection of retinal vessels in color fundus images leveraging the potential of computer assisted diagnosis [5, 11] and assist in routine screening [3, 4]. Challenge: These methods [5–7,9,10] predominantly use image filters, vector geometry, statistical distribution studies, and machine learning of low-level features for vessel detection, thus being heavily subjective and image quality dependent. The primary challenge here is to identify both coarse and fine vascular structures. For achieving this we propose to learn photon-tissue interaction response of retinal vessels for discriminating them from other tissues. The problem is formally defined in § 2. Approach: Our apprach of achieving a solution to retinal vessel detection is through inductive transfer learning of statistical physics of photon-tissue interaction. Fig. 1 illustrates an example of exhaustive retinal vessel detection using
our approach. The Poisson distribution of photon sensing using CCD or CMOS digital sensors is well established through theoretical and experimental studies [12, 13]. Although tissue specific photon interaction models have been employed for discrimination of human pancreatic tissues [14], yet such approaches have not been used in related prior art [5–7, 9, 10]. Here we introduce a transfer learning framework [15] to achieve a solution, whereby (i) initially a set of weak learners accomplish the source task of locally learning the Poisson process parameters guiding the photon-tissue interaction statistical physics model, and (ii) subsequently a strong learner uses this knowledge to accomplish the target task of learning the Poisson process parameter space characterizing different tissues. The problem statement in §2 justifies our transfer learning approach and details of the solution are discussed in §3. This approach translates directly as a robust method for detection of retinal vessels as is experimentally reported in §4 along with discussion of findings. Finally we have concluded the work along with a summary of its impact in §5. 2. PROBLEM STATEMENT Let us consider a color fundus image acquired by an RGB sensor to be I. At any location (x, y) on the image, the color information is represented using a vector c. Typically for an RGB image, this is a 3-tuple vector, c = {dR , dG , dB } where dR , dG and dB respectively indicate the intensity sensed by opto-electronic sensors responsive to red, green and blue optical spectral bands. The optical spectral filters are arranged following the Bayer pattern and sensor readings are ensembled to represent the local statistics. These band specific readings d[λ] are stochastic in nature and follow a statistical physics model Φ. As defined in [12], this model is a function of the optical response of the fundus ophthalmoscope and camera, spectral incident irradiance pattern and spectral response of photon-tissue interaction. If imaging parameters do not vary, then the only variable factor affecting Φ is response of photon-tissue interaction. However, this model Φ is not unique over the complete range of the color fundus image and varies locally as has also been observed in related Poisson intensity and density estimation problems [13, 16]. Thus we propose to learn Φ locally from c using a set of weak learners to have a set Θ = {Φ}. Subsequently this knowledge represented in the set Θ can be learnt using a set of annotated training images and a strong learner for creating a tissue specific photon interaction statistical physics model, capable of discriminating vessels from non-vascular tissue. This approach can be formally defined accordingly: Formal definition: The probability of detecting a vessel p(ω|I, (x, y)) is the response of a function H(ω|Θ, I; {I}train) that predicts tissue of type ω ∈ {vessel, non-vascular} in a sample image I using knowledge of photon-tissue interaction models Θ = {Φ} locally learnt on I, and the previously learnt knowledge of Θ from a set of training examples {I}train .
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3. PROPOSED SOLUTION This formal definition can be modelled as an inductive transfer learning problem. Transfer learning primarily deals with improving the performance of a machine learning task by including knowledge acquired while solving a related task at an earlier stage [15]. The task from which knowledge is transferred is generally referred to as the source task, while the task which imbibes this knowledge is referred to as the target task. The source task is accomplished on the source domain while the target task is accomplished on the target domain. In our approach of formulating H(ω|Θ, I; {I}train), the source task is to locally estimate the photon-tissue interaction statistical physics model and transfer the knowledge Θ to the target task. The target task is to probabilistically detect vessels in a new image I utilizing the function H(ω|Θ, I; {I}train) that has previously learnt Θ for the different classes of tissues using {I}train . The source domain and target domain are set of RGB color fundus images and accordingly this transfer learning problem can be categorized to be an inductive transfer of knowledge. The methodology of realizing source and target tasks are presented next. 3.1. Source task: Modeling statistical physics of PhotonTissue interaction The rate of photon induced electron generation (ρ) at a site on the camera photosensor fixed with a fundus ophthalmoscope can defined as [12]
ρ=
Z Z Z λ
y
B(x, y, λ)Sr (x, y)q(λ) dx dy dλ
(1)
x
where (x, y) are continuous coordinates on the sensor plane, q(λ) is the internal quantum efficiency of the detector (electrons / Joule) as a function of wavelength of incident radiation (λ). Sr (x, y) is the spatial response of the collection site on the sensor. The spectral irradiance pattern B(x, y, λ) (Watts / unit area) incident on the sensor is modelled as B(x, y, λ) = [R(x, y, λ)L(x, y, λ) ∗ p(x, y, λ)]t(λ)
(2)
where ∗ is the spatial convolution operator, p(x, y, λ) is the point-spread-function of the fundus ophthalmoscope and camera optics, and t(λ) is the spectral transmission of the optics. R(x, y, λ) is the spatially varying spectral reflectance of the surface being imaged and L(x, y, λ) is the spatially varying illumination model. The photon induced voltage (D) sensed and subsequently read out of the camera sensor circuitry is D = (KρT + NDC + NS + NR )A + NQ , where K is the external quantum efficiency of the sensor (Volts / electron), T is the typical integration time of the sensor, NDC is the dark current noise, NS is the shot noise, NR is the readout noise, A is the amplification factor of the readout
circuitry, NQ is the quantization noise of the ADC. In precalibrated sensors, NDC , NS , NR , NQ
