Othman Alhusain 
  
CORRECTION OF NON-LINEAR DISTORTION IN DIGITAL IMAGES USING A PROPOSED 
NORMALIZATION ALGORITHM 
Othman Alhusain 
Budapest University of Technology and Economics, Dept. of Photogrammetry and Geomatics, 
Muegyetem rkp. 3, I. 24., H-1521 Budapest, Hungary 
Email: alhusain@eik.bme.hu 
  
Working Group IC-4 
KEY WORDS: Algorithms, Corrections, Sensors. 
ABSTRACT 
In this paper, image formation will be investigated in detail. Data captured is a representation of data collected by two 
kinds of sensors widely in use in remotely sensed image processing applications. These are space borne optical sensors 
and one example of electro-optical sensors used in medical imaging applications. The investigation shows that non- 
linear distortion is materialized in two aspects related to data measured by the sensor system. These are the intensity of 
the signal measured at a given pixel and the location (coordinates) of that measured signal. The existence of such 
distortion is strange enough, taking into consideration that the algorithms implemented in image formation are all well 
designed and based on sound mathematical foundations. 
The algorithm proposed to correct these non-linear discrepancies is a phase that follows data capture and image 
formation. It functions as a correction stage for non-linear distortion before the image is rendered into its final form. 
The principal idea of the algorithm is to perform a normalization process on either the coordinates of the measured data, 
the value (intensity) of the measured data, or on both. In the process, at each pixel, the values (coordinates, intensity) 
associated with the measured data are compared to those of a reference and/or neighbouring pixels, and are modified 
accordingly. Performing the normalization algorithm has resulted in significant reduction of non-linear distortion in the 
generated images. In many cases it has resulted in total elimination of the distortion. 
1 INTRODUCTION 
Compensation for non-linear distortion is best done through the optimum design of the circuitry (hardware) of the 
different elements involved in the data capture and image formation of the imaging system. Unfortunately, this goal is 
impossible to attain solely through the hardware alone due to factors related to the characteristics of the hardware 
implemented and to those of the captured data itself. A more amenable solution to the non-linearity problem can be 
achieved through the implementation of algorithms that correct image non-linearity caused by different stages of the 
imaging system. Algorithmic corrections are especially more attractive than hardware oriented solutions due to the fact 
that to implement them there is no need for any change on the hardware already installed. Algorithms are also easily 
modified when the need arises in later stages, and in many cases, are even less expensive to utilize. 
Non-linear distortion happens in imaging systems mainly due to two reasons. First, non-linear and variable response of 
the "sensing" elements in the sensor system to different intensities of signals. This kind of distortion depends on 
physical properties of the "sensing" elements and can be modeled and compensated for with reasonable accuracy. 
Second, and most significant, is that sensors utilized in imaging systems, whether these are far-range (air- space borne) 
or close-range (terrestrial, medical), are generally designed in a way that each sensor is made up of rows or arrays of 
individual sensing elements ranging from few to several tens to provide for complete coverage of the scanned area. 
Theoretically, individual sensing elements assembled in a single sensor are designed to be identical when they are 
required to perform the same function, as to giving equal output when scanning the same or similar areas. However, 
practically this is a goal hard to achieve and maintain, especially with aging of the sensor. This non-conformity among 
sensing elements results in variations in the physical and electronic characteristics of the individual sensing elements 
which in turn result in changing the conditions at which signals are measured, and consequently can lead to significant 
fluctuations in the response of each sensing element when measuring the same signal. Meanwhile in the ideal case the 
response of each sensing element and measurement of the signal should be identical. Thus non-linear spatial distortions 
cause noticeable non-uniformities in captured images. Various methods to correct for spatial non-uniformities utilize the 
concept of increasing or decreasing the density and/or intensity of the captured signals (events) in specific areas in the 
image where the distortion is most apparent (Graham et al., 1978, Morrison et al., 1971). However, non-uniformity 
  
12 International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part Bl. Amsterdam 2000. 
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