Example 1: Distortion
First of all the distortion, which is in the context of asexual reproduction the common technique, shall be described. Within the second example the distortion operation is used together with other operations like cutting and RST (rotation-scaling-transformation) to perform a asexual reproduction.
Usually distortion operations are local filters which change the arrangement of the segments of the image. In contrast to a RST transformation in which the arrangement of the segments remain constant. By their local character they are stated through starting point, end point and a symmetrical range of application, which is defined by the distance of the connecting line between starting and end point. This range of application is commonly known as the width of the paintbrush of the operation. The straight line between both picture points shall be regarded, a special definition of curve forms shall be omitted. The range of application is thereby defined as a range within the image which is seen in image 1 within the blue limited areas.
Image 1) Range of Application of a distortion operation.
Metamorphoses images are characterized by hard color transmissions, hard contrasts, curved lines and monochrome segments. The usage of a fractal distortion operation would lead to interrupted and irregular distorted lines. The usage of a fractal distortion filter is mainly waived
Instead of using a fractal distortion filter a so-called freehand distortion filter should be used through which the image segment is transformed parallel to the movement given by the starting - and the end point.
An individual selected for a mutational reproduction by a distortion operation has to be assigned a region, where the operation should take place. This might occur by a random process which selects a starting point in the picture. Since metamorphoses images can be seen as objects before a background it might occur, that a point in the background is selected as starting point. The background is defined as white, hence the distortion operation would show no effect. An automatic exemption by defining the color white as outer area is not wise for all pictures which contain the color white.
For this reason it is better to describe a section of the picture manually in which the starting point may occur. So regions of interest are build up. The ROIs in a metamorphoses image M-k may be described as ROI(k,i).i from {1,...} which can be combined to ROI (k) = {ROI (k,i) | i = 1, ...}.
ROIs can be seen as rectencular regions in a picture, but they also could have other forms like circles or ellipses.
Image 2) Simple ROI
Hence ROI(k,i) is specified by two points which designate the opposite edges of a rectangle. P(u) is the left lowered point, P(o) is the upper right point:
ROI (k,i) = (P (u | k,i), P (o | k,i)).
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An overlapping ROI is allowed, this means a point, which is laid in one ROIS may be in another ROI.
Image 3) Example for a overlapping ROI
Generally the operation should be limited to the ROI to maintain the local character of the operations. The distortion operations are hence triggered in such a way, that starting and end point of the operation lays within the ROI. Results, generated by the thickness of the paintbrush and jut out of the frame are allowed.
After the selection of an individual for a asexual reproduction a subset of the given ROIS is selected in which the mutation operation should occur. If exactly one distortion operation is performed it has to be determined next, how many operations should be applied on the selected ROIs.
Both operations can be determined together by a mutational vector s(k) of the image M-k. This vector defines the number m(i) of single mutations in a given ROI(k,i). m(i)=0 means, that in this ROI no mutation takes place:
s (k) = ( (ROI (k,i), m (i)) | m (i) aus {0, 1, ...}, i = 1, ...).
The m(i) distortion-operation V (k,i,j) in the ROI(k,i) may be described as a list, which encodes the sequence of the occurrence of the performance of the operations. The operations can not take place independently on the given ROI. Distortions are always applied on the actual image. Hence the mutational vector of the image M-k is:
s (k) = ( (ROI (k,i), V (k,i)) | i = 1, ...),
V (k,i)) = (V (k,i,j) | j = 1, ..., m (i); m (i) aus {0, 1, ...}).
From the ROI seen in image 2) under application of an example mutational vector an result seen in image 4). The vector refers only to this ROI.
Image 4) Results of a mutation within a ROI
In the following Image once again the performance of an asexual replication is portrayed in a survey. Starting with the selection of a parent individual from the parent population, followed by the selection of the ROI on which the distortion operation is limited. The mutation is performed as a sequence of distortion operation. These are limited to the ROIs. The result is stored as an offspring of the selected parent individual and transferred into the interim population.
Image 5) Survey over the asexual reproduction.
