27-03-2014, 11:40 AM
LINEAR VERSUS NON-LINEAR DIGITAL IMAGE PROCESSING METHODS
[attachment=60522]
ABSTRACT
Digital image processing methods can be classified either as linear or as non-linear. The
robust mathematical basis for the linear approach justifies the preference for linear methods,
although the non-linear techniques are spreading. Analysing the image gathering chain, the
non-linearity of the intensity to voltage conversion, known as the gamma function, is referred
but its consequences usually disregarded. This may put in question the validity of the straight
linear approach this chain is not, and explain why apparent formally perfect techniques often
lead to inconclusive or unexpected results. On the other hand, non-linear approaches, as those
based on mathematical morphology, are gaining wider preference, mainly due to their
simplicity and robustness.
INTRODUCTION
Digital images result from an analog to digital conversion of an electric signal from the image
sensor. The digital format is convenient for archiving, transmission and processing with
complex algorithms not available in the analog world.
The Cathode Ray Tube (CRT) is the reference device for display of electronic images. Some
characteristics of CRTs are embedded in the electronic image applications, and digital image
processing could not escape. The main point of this paper concerns the use of a non-linear
pre-correction of the voltage signal. This is usually referred, but not accounted for (Fernandes,
2004).
This non-linearity in the chain leads to a non-linear process, even when the algorithm that
supports the processing is formally linear. The results of a supposed linear technique fail
often, just for a small differences in the image, and that should not happen in a linear
approach.
THE LINEAR DILEMMA
Using digital image data without gamma compensation, leads to algorithms with hidden non-
linear characteristics, lose their intended purpose and producing distorted results.
If the algorithm uses pure numerical data, and so unrelated to image intensity, the linearity of
the process is guaranteed, but the results cannot be related linearly to the image information
(that is intensity) nor translated into an image of the same type.
CONCLUSIONS
Linear algorithms in image processing may fail to produce the envisaged results but, instead
of simply abandoning the approach, using correctly linear coded images may validate the
technique. Probably, many perfectly valid schemes were discarded just for lack of results due
to the implicit non-linear chain in the image acquisition equipment.
[attachment=60522]
ABSTRACT
Digital image processing methods can be classified either as linear or as non-linear. The
robust mathematical basis for the linear approach justifies the preference for linear methods,
although the non-linear techniques are spreading. Analysing the image gathering chain, the
non-linearity of the intensity to voltage conversion, known as the gamma function, is referred
but its consequences usually disregarded. This may put in question the validity of the straight
linear approach this chain is not, and explain why apparent formally perfect techniques often
lead to inconclusive or unexpected results. On the other hand, non-linear approaches, as those
based on mathematical morphology, are gaining wider preference, mainly due to their
simplicity and robustness.
INTRODUCTION
Digital images result from an analog to digital conversion of an electric signal from the image
sensor. The digital format is convenient for archiving, transmission and processing with
complex algorithms not available in the analog world.
The Cathode Ray Tube (CRT) is the reference device for display of electronic images. Some
characteristics of CRTs are embedded in the electronic image applications, and digital image
processing could not escape. The main point of this paper concerns the use of a non-linear
pre-correction of the voltage signal. This is usually referred, but not accounted for (Fernandes,
2004).
This non-linearity in the chain leads to a non-linear process, even when the algorithm that
supports the processing is formally linear. The results of a supposed linear technique fail
often, just for a small differences in the image, and that should not happen in a linear
approach.
THE LINEAR DILEMMA
Using digital image data without gamma compensation, leads to algorithms with hidden non-
linear characteristics, lose their intended purpose and producing distorted results.
If the algorithm uses pure numerical data, and so unrelated to image intensity, the linearity of
the process is guaranteed, but the results cannot be related linearly to the image information
(that is intensity) nor translated into an image of the same type.
CONCLUSIONS
Linear algorithms in image processing may fail to produce the envisaged results but, instead
of simply abandoning the approach, using correctly linear coded images may validate the
technique. Probably, many perfectly valid schemes were discarded just for lack of results due
to the implicit non-linear chain in the image acquisition equipment.