Keywords: non-linear diffusion, fuzzy-rule based diffusion coefficient, thermal image processing.

This paper presents an adaptive, fuzzy-rule based diffusion model which can be used to enhance thermal images (thermograms). Infrared thermography provides images in which zones of interest appear sometimes as subtle signatures. Signals in the thermal bands are intrinsically weak with respect to visible bands. Infrared (IR) images can be degraded not only by the error of the imaging processes but by the non-uniform properties of the surface where data is collected. At the pixel level, the noise in the thermal image is additive, has a Gaussian nature and consists of high frequencies with respect to the useful signals [1]. Probably the most common pre-processing procedure is noise smoothing with a partial differential equation (PDE) based diffusion model. Smoothing precedes the higher level image processing techniques such as edge detection, image segmentation, classification, object identification, etc. Smoothing allows an exchange of information between neighbouring parts of an image, thus extending the effect of local data to a wider area. The main problem of smoothing is the dilemma of concurring image properties, such as sharpness and smoothness, respectively. Removing noise in an image, the fine details are usually also filtered out. By enhancing the edges and fine structures, on the other hand, the noise will also be amplified. To solve the problem, many approaches have already been developed [2]. In a thermal image edges are originally blurred and consequently they are hard to detect with the classical edge-preserving algorithms. In this work a PDE-based non-linear diffusion algorithm is combined with a fuzzy-diffusion coefficient. The proposed smoothing technique is a non-linear time-variant system, in which the diffusion coefficient depends on the local characteristics of the image. The proposed technique belongs to the fuzzy extensions methods [3,4]. The smoothing effect of the diffusion corresponds to the user demands: for example removing noises or smoothing only the predefined intensity region(s) without blurring and moving edges. The proposed fuzzy-technique results a strongly non-linear diffusion function which can be formulated in a user-friendly way.

Human activity involves the loss of energy in the environment. Many industrial processes also release massive amounts of energy in water or in the air. Thermal sensing is of prime importance to detect, identify and analyze these thermal manifestations. Relatively few researchers have visualized the fluid flow field using IR imaging [5]. In this paper the IR thermography has been employed to visualize the turbulent steam flow. The IR detector works in the long wave band (8-14 μm) which is a part of an atmospheric window. In this wave band the water vapour is transparent therefore a hot steam jet can be visualized if it contains condensed water droplets. Detection of radiation of droplets requires temperature difference between the steam jet and the background. In an axisymmetric flow, the path length normal to the imaging plane varied with spatial location. An increase in net intensity could be manifest from variations in temperature and mass concentration along, and normal to the imaging plane, thereby leading to an ambiguity in interpreting the intensity images in such flows.

This paper shows that the fuzzy-rule based diffusion method enhanced the thermogram of the turbulent pattern of an instantaneous flow. The high frequency components of the stream have been retained, while the intensity variation of the background has been attenuated. The output image has more contrast compared to the commonly used Gauss-type low-pass filtering. The verification of this method is based on the wavelet reconstruction of the high frequency image-details and on the comparison of energy contents of the images. An averaging of consecutive time series images approximates a smooth map of the Reynolds-averaged flow. With the fuzzy-rule based filtering technique the remaining high frequency intensity variations of the highest intensities can be smoothed without reducing the energy content of the image. The filtered thermal image and the image of diffusion coefficients can provide a firm base for segmentation or object detection procedures.

1

X. Maldague, "Theory and Practice of Infrared Technology for Nondestrucive Testing", Wiley, New York, 2001.

2

G. Aubert, P. Kornprobst, "Mathematical Problems in Image Processing", Springer, New York, 2002.

3

H.R. Tizthoosh, "Fuzzy-Bildverarbeitung", Springer, Berlin, 1998.

4

K. Arakawa, "Fuzzy-Rule Based Image Processing with Optimization", in "Fuzzy Techniques in Image Processing", E.E. Kerre, M. Nachtegael (Editors), Physica-Verlag, Heidelberg, New York, 2000.

5

V. Narayanan, R.H. Page, J. Seyed-Yagoobi, "Visualization of Air Flow Using Infrared Thermography", Experiments in Fluids, 34, 275-284, 2003. doi:10.1007/s00348-002-0557-x

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