Unsupervised document image binarization using a system of nonlinear partial differential equations

Image Trinarization Using a Partial Differential Equations: A Novel Approach to Automatic Sperm Image Analysis

“…The present work extends the PDE based framework for image processing previously established for document image binarization [5,6,8]. The application of CASA raises the issue of image trinarization, whereby an image data is classified into three distinct classes.…”

“…The model is also subjected to zero-flux boundary conditions along all boundaries of the domain. This choice of boundary condition ensures smoothness at the boundaries and is motivated by previous works [5,6,8]. Explicitly, the boundary conditions are given by,…”

“…Figure 2 illustrate the phase space dynamics of the source term. This structure is an extension of the Fitzhugh-Nagumo model used in previous works [5,6,8]. The source term exhibits five steady states; u = 0, u = a, u = b, u = c and u = 1.…”

“…This work builds on previous works by the author [5,6,8] where PDE models were used for document image binarization, implementing global thresholding, locally adaptive thresholding and a nonlinear system of equations which self-governed the model parameters resulting in an unsupervised methodology. The approach was also extended to time fractional PDEs presented in [7].…”

“…More recently, PDEs have become a useful tool in image processing. Applications in image denoising, restoration, inpainting, remote sensing applications, document image binarization, [1,2,3,4,5,6,7,8,9,10], are a small subset of applications that illustrate the value of using a PDE framework to attain novel image processing algorithms. Additionally, research on processing medical images, such as ultrasounds and MRIs [11,12,13].…”