Research Interests

Peihua Qiu's Research on Image Processing


In the image processing literature, there are different ways to describe an image and image contaminations (e.g., Markov random fields, diffusion equations). My research on image processing mainly uses the statistical tool of jump regression analysis (JRA). A 2-D monochrome image can be regarded as a surface of the image intensity function with jumps at the outlines of image objects. Usually, observed images contain pointwide noise, spatial blur, and other types of contamination. Therefore, they can be described well by 2-D JRA models; and jump detection and jump surface estimation methods in JRA can be applied directly to edge detection and image denoising in image processing. As noted by a well known computer scientist in his book Pratt (2007, Digital Image Processing, 4th ed., Wiley), many methods in the image processing literature are ad hoc in nature, and we do not really understand when these methods will work well and when they will fail. The JRA framework should be useful in establishing some necessary theory to support the related image processing methodologies.

My book Qiu (2005) devotes three chapters to the JRA and two chapters to the related image processing techniques. It describes the connections and differences between JRA and image processing, and it is the first book trying to bridge the gap between the two areas. Besides edge detection (e.g., Qiu and Bhandarkar 1996, Qiu 2002, Sun and Qiu 2007, Kang and Qiu 2014) and image denoising (e.g., Qiu 1998, Qiu 2004, Gijbels, Lambert and Qiu 2006, Qiu 2009, Qiu and Mukherjee 2010, Mukherjee and Qiu 2015), my co-authors and I have also done much research on the topics described below.

Blind image deblurring:
Blind image deblurring tries to reconstruct the true image from its observed but degraded version when both pointwise noise and spatial blur are present and when the blurring mechanism described by a point spread function (psf) is not fully specified. Most existing methods assume that either the psf is known or it follows a parametric model. Hall and Qiu (2007a,b) and Qiu (2008) suggested some blind image deblurring procedures under more flexible assumptions; thus, they can be used in more applications. For instance, my current research on this topic allows the psf to be nonparametric and varying over location (Qiu and Kang 2015).

Segmentation of microarray images:
Recently, microarray image analysis is popular for genetic research. However, gene expression data generated by existing microarray image segmentation procedures are often unreliable, due to their inability to remove noise efficiently. We demonstrated this fact and proposed a more reliable segmentation procedure for analysing microarray images (Qiu and Sun 2007). We also proposed a post-smoothing procedure to make the existing edge detection techniques to be useful for microarray image analysis (Qiu and Sun 2009).

Image registration:
Image registration aims to map one image to another taken from a same scene. It is a fundamental task in many imaging applications. Most existing image registration methods assume that the mapping transformation has a parametric form or satisfy certain regularity conditions (e.g., it is a smooth function with the first-order or higher order derivatives). They often estimate the mapping transformation globally by solving a global minimization/maximization problem or by using a global smoothing technique. Such global smoothing methods usually cannot preserve singularities (e.g., discontinuities) and other features of the mapping transformation well. Further, the ill-posed nature of the image registration problem, i.e., the mapping transformation is not well defined at certain places (e.g., at places where the true image intensity surfaces are straight), is undisclosed by such methods. Recently, we suggest handling the image registration problem locally, by first studying local properties of a mapping transformation. To this end, we suggest the concept of non-degerate pixels. A local smoothing method for estimating the mapping transformation is proposed accordingly (Xing and Qiu 2011). Because of the flexibility of local smoothing, our method does not require many regularity conditions on the mapping transformation. In a recent paper (Qiu and Xing 2013a), this topic is further studied. several concepts, including the 2-D degenerate pixels, 2-D partial degenerate pixels, 1-D degenerate pixels, and 1-D partial degenerate pixels, are proposed for describing the local properties of the mapping transformation T. The relationship among these concepts and the statistical properties of the estimated T are also studied. In Qiu and Xing (2013b), we further demonstrated that non-degerate pixels were ideal features for image registration, compared to some other commonly used features.

3-D image analysis:
In various applications, including magnetic resonance imaging (MRI) and functional MRI (fMRI), 3-D images get increasingly popular. To improve the reliability of subsequent image analyses, 3-D image denoising is often a necessary pre-processing step. In the literature, most existing image denoising procedures are for 2-D images. Their direct extensions to 3-D cases generally can not handle 3-D images efficiently, because the structure of a typical 3-D image is substantially more complicated than that of a typical 2-D image. For instance, edge locations are surfaces in 3-D cases, which would be much more challenging to handle, compared to edge curves in 2-D cases. We propose a novel 3-D image denoising procedure based on local approximation of the edge surfaces using a set of surface templates (Qiu and Mukherjee 2012). An important property of this method is that it can preserve edges and major edge structures (e.g., intersections of two edge surfaces and pointed corners) well.

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