#### Spatial Operators – Handling Edge Pixels

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We run into problems when we take all of the pixels in a box around an input pixel and that pixel is close to one of the edges of the image. Let’s look at some strategies to deal with edge pixels.

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We run into problems when we take all of the pixels in a box around an input pixel and that pixel is close to one of the edges of the image. Let’s look at some strategies to deal with edge pixels.

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We can describe the relationship between a 3D world point and a 2D image plane point, both expressed in homogeneous coordinates, using a linear transformation – a 3×4 matrix. Then we can extend this to account for an image plane which is a regular grid of discrete pixels.

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The linear algebra approach we’ve discussed is very well suited to MATLAB implementation. Let’s look at some toolbox functions that can simulate what cameras do. If you are using a more recent version of MVTB, ie. MVTB 4.x then please change>> cam.project(PW ‘Tcam’, transl(0.1, 0, 0)) to >> cam.project(PW ‘pose’, transl(0.1, 0, 0)).

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If we look at a binary image we can easily see distinct regions, that is, sets of pixels the same color as their neighbours. We call these blobs and they’re an important way of achieving an object rather than pixel view of the scene. We can describe these blobs by their area, centroid position, bounding […]

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We introduce spatial operators by a simple example of taking the average value of all pixels in a box surrounding each input pixel. The result is a blurring or smoothing of the input image.

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An important class of operations are monadic, which map an input image to an output image of the same size by applying the same function to every pixel.

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There are a lot of pixels in a typical image which makes them take up a lot of memory. Images can be compressed to take up less storage. Compression can be lossless or lossy, where we tradeoff size for quality.

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MATLAB normally deals with matrices of floating point numbers. An image is typically represented by an array of small integer values, pixel value or greyscale values, which have a limited dynamic range and special rules for arithmetic.

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We can use MATLAB to display a profile of brightness along a line in the image.

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So far we have taken a linear combination of pixels in the box around the input pixel, but non-linear operations like sorting and ranking the pixel values also prove to be very useful. We look at the median filter which is much better at removing salt and pepper noise from image than simple smoothing.