Computer Studies Image_Interpolation_using_Mathematical_M.pdf

# In general a dilation results in an enlarged version

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In general, a dilation results in an enlarged version of the input object. The net effect of an erosion is to shrink or erode the input object. The structuring element B can be of any size or shape and is chosen depend- ing on the image and the application. The origin of the strel is also important, as it states how the strel is positioned relative to the examined pixel. 2.2 The hit-miss transform The hit-miss transform ” is a morphological operator used extensively in our algorithm. It is defined in terms of two disjoint structuring elements: one for the erosion of object pixels ( B ), and one for the erosion of background pixels ( C ). Its definition is: A ( B, C ) = ( A B ) ( A c C ) , (2) with A c the complement set of A . With the hit-miss transform it is possible to detect specific shapes in the image. We will use it to detect corners. To detect the upper-left corners of an object, we use the structuring elements (a) and (b) of fig. 2. An alternative for strel C for the corner detection is the use of the structuring element (c) in fig. 2. 3 A is the set of the coordinates of the foreground pixels (value 1) in an image. In the remainder of this paper, we will often simply refer to A as “the (binary) image”.

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(a) Strel B (foreground) (b) Strel C (background) (c) Strel C 0 (b.g. alternative) Fig. 2. Upper-left corner detection with the hit-miss transform. Specific strels are used. The black squares are pixels of the strel; the cross is the origin of the strel Fig. 3. The difference between “jagged corners” and “real corners” (encircled) The result of the hit-miss transform is an image in which the foreground pixels indicate the position of the upper-left corners. Alternatively, the output can also be viewed as a set of corner coordinates. We further refer to this set as a corner map . In our method we apply the hit-miss transform several times, with rotated versions of the structuring elements in fig. 2 in order to produce four corner maps (upper-left, upper-right, lower-left and lower-right). 3 Binary interpolation scheme: mmINT In this section we summarize the mm int method presented in [12]. Its purpose is to remove the jagged edges from a pixel replicated image, by swapping specific pixels from background to the foreground and vice versa. We consider the most frequent colour in the image to be the background. Different steps can be distinguished in the algorithm: 1. Pixel replication : First the image is pixel-replicated by an integer factor M . The resulting image contains strong staircase patterns because of the pixel replication (see for example fig. 1). 2. Corner detection : Using a combination of hit-miss transforms, the algo- rithm determines the positions of corners, both real and false (due to jaggies) in the image. 3. Corner validation : Some corners found in the preceding step are real cor- ners , which have to be retained in the interpolated image. For example, the corners of the door and walls in fig. 3 are real corners. The corners detected on the roof are jagged corners , because the ideal roof is a diagonal line. The aim of corner validation is to distinguish false corners from real ones.
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• Fall '18
• William
• Image processing, Mathematical morphology, Digital geometry

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