Getting some elements out of an existing array and creating a new array out of them is called filtering. If the value at an index is True that element is contained in the filtered array, if the value at that index is False that element is excluded from the filtered array. Because the new filter contains only the values where the filter array had the value Truein this case, index 0 and 2.

In the example above we hard-coded the True and False values, but the common use is to create a filter array based on conditions. We can directly substitute the array instead of the iterable variable in our condition and it will work just as we expect it to.

If you want to report an error, or if you want to make a suggestion, do not hesitate to send us an e-mail:. A boolean index list is a list of booleans corresponding to indexes in the array. HOW TO. Your message has been sent to W3Schools.

**Special Case Median Filtering**

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Copyright by Refsnes Data. All Rights Reserved. Powered by W3.Either size or footprint must be defined. We adjust size to the number of dimensions of the input array, so that, if the input array is shape 10,10,10and size is 2, then the actual size used is 2,2,2.

When footprint is given, size is ignored. The array in which to place the output, or the dtype of the returned array. By default an array of the same dtype as input will be created. The mode parameter determines how the input array is extended when the filter overlaps a border. By passing a sequence of modes with length equal to the number of dimensions of the input array, different modes can be specified along each axis.

The valid values and their behavior is as follows:. The input is extended by filling all values beyond the edge with the same constant value, defined by the cval parameter. Default is 0. A value of 0 the default centers the filter over the pixel, with positive values shifting the filter to the left, and negative ones to the right.

By passing a sequence of origins with length equal to the number of dimensions of the input array, different shifts can be specified along each axis. Ignored if footprint is given. Has the same shape as input.

Previous topic scipy. Last updated on Dec 19, Created using Sphinx 2.Axis or axes along which the medians are computed. The default is to compute the median along a flattened version of the array.

A sequence of axes is supported since version 1. Alternative output array in which to place the result. It must have the same shape and buffer length as the expected output, but the type of the output will be cast if necessary. If True, then allow use of memory of input array a for calculations. The input array will be modified by the call to median. This will save memory when you do not need to preserve the contents of the input array. Treat the input as undefined, but it will probably be fully or partially sorted.

Default is False. If this is set to True, the axes which are reduced are left in the result as dimensions with size one. With this option, the result will broadcast correctly against the original arr. A new array holding the result. If the input contains integers or floats smaller than float64then the output data-type is np. Otherwise, the data-type of the output is the same as that of the input. If out is specified, that array is returned instead.

Returns the median of the array elements. New in version 1. See also meanpercentile. Previous topic numpy. Last updated on Jul 26, Created using Sphinx 1.By using our site, you acknowledge that you have read and understand our Cookie PolicyPrivacy Policyand our Terms of Service.

Signal Processing Stack Exchange is a question and answer site for practitioners of the art and science of signal, image and video processing.

It only takes a minute to sign up. I have read in many places that Moving median is a bit better than Moving average for some applications, because it is less sensitive to outliers. I wanted to test this assertion on real data, but I am unable to see this effect green: median, red: average. See here:.

Here's the sample audio data test. Here's the Python code:. I have tried with various values for Window width here in the code :and it was always the same: the moving median is not better than moving average i.

Can you provide an example showing that moving median is less sensitive to outliers than moving average? And if possible using the sample. WAV file data-set download link. Is moving median always less sensitive to outliers?

However, if you have a large spike, then taking the median won't help eliminate the spikes. Notice how the the median of the all the 40s is For example, take the 1st The left values are 5,6 and the right values are 40,40, so we get a sorted dataset of 5,6, 40 ,40,40 the bolded 40 becomes our median filter result.

You also wanted an example for the median filter to work. So, we will have a short spike. Try this:. You can see that the median filter did filter out the single large spike, while the spike skewed the average filter's results for entries 4,5,40,and,6. This isn't really an answer, but I thought I'd report what I'm seeing and ask for more information.

So what you're getting in the plots you show is not so much the median value, but is more like an envelope of the signal. The second issue is that the signal actually seems to be part of the signal. If I zoom into the blip then this is what I see:. From the plot below, the best performing is the length one.

Otherwise the effect of the glitch is still present. The only thing I can see wrong now is that the "envelope" doesn't match the true envelope as well as I'd like.

A better envelope detector might improve this e. What you said is correct - moving median is less sensitive to outliers, where an outlier is usually a single point in time series that is very different from all others, which may be due to some kind of error.

However, moving median can be even more sensitive to short term significant spikes that span several points, especially when they span more than half of the moving window.A long while back I tested some code to apply a mean filter to a grayscale image written in Julia Testing Julia for speed iiiand compared against three other languages: C, Fortran, and Python. This is a continuation of those posts and looks at the code in the other languages. First on the list is Python. The code below has two parts, the main program, and the function meanFilter.

One of the problems with Python is that even though it is a simple language from the perspective of language structure, it suffers from some usability issues. First is the fact that the act of reading in the text image involves a lot of somewhat cryptic code. Natively to read a series of integers from a file is not exactly trivial. It reads the image in as lines, and then splits the lines up into numbers.

Numpy is of course the Python package incorporating n-dimensional array objects. Of course if we used numpy to its entirety, we could just use it to read in the text image:.

It is challenging to use Python effectively for image processing without the use of numpy. The function meanFilter processes every pixel in the image apart from the image borders. Python uses the range function to determine the list of loop iterators for the for loops. The result is then converted to an integer, and assigned to the filtered image.

After the image has been processed, the filtered image is output to a text file. Overall, the Python algorithm works, although it is slow. Since I ran this code previously, the run-time has improved faster machine likely.

### Numpy statistical functions

There are obviously more efficient ways to write this code in Python e. You are commenting using your WordPress. You are commenting using your Google account. You are commenting using your Twitter account. You are commenting using your Facebook account. Notify me of new comments via email.

Notify me of new posts via email. This site uses Akismet to reduce spam.It means that for each pixel location in the source image normally, rectangularits neighborhood is considered and used to compute the response. In case of a linear filter, it is a weighted sum of pixel values.

In case of morphological operations, it is the minimum or maximum values, and so on. The computed response is stored in the destination image at the same location. It means that the output image will be of the same size as the input image. Normally, the functions support multi-channel arrays, in which case every channel is processed independently.

Therefore, the output image will also have the same number of channels as the input one. Another common feature of the functions and classes described in this section is that, unlike simple arithmetic functions, they need to extrapolate values of some non-existing pixels. For example, if you want to smooth an image using a Gaussian filter, then, when processing the left-most pixels in each row, you need pixels to the left of them, that is, outside of the image.

OpenCV enables you to specify the extrapolation method. For details, see the function borderInterpolate and discussion of the borderType parameter in the section and various functions below.

## Code review

The class BaseColumnFilter is a base class for filtering data using single-column kernels. Filtering does not have to be a linear operation. In general, it could be written as follows:. The class only defines an interface and is not used directly. Instead, there are several functions in OpenCV and you can add more that return pointers to the derived classes that implement specific filtering operations. Those pointers are then passed to the FilterEngine constructor.

While the filtering operation interface uses the uchar type, a particular implementation is not limited to 8-bit data. The class BaseFilter is a base class for filtering data using 2D kernels.

The class BaseRowFilter is a base class for filtering data using single-row kernels. The class FilterEngine can be used to apply an arbitrary filtering operation to an image.

Thus, the class plays a key role in many of OpenCV filtering functions. This class makes it easier to combine filtering operations with other operations, such as color space conversions, thresholding, arithmetic operations, and others. By combining several operations together you can get much better performance because your data will stay in cache.

For example, see below the implementation of the Laplace operator for floating-point images, which is a simplified implementation of Laplacian :. If you do not need that much control of the filtering process, you can simply use the FilterEngine::apply method. The method is implemented as follows:. Unlike the earlier versions of OpenCV, now the filtering operations fully support the notion of image ROI, that is, pixels outside of the ROI but inside the image can be used in the filtering operations.

For example, you can take a ROI of a single pixel and filter it. This will be a filter response at that particular pixel. Explore the data types. To make it all work, the following rules are used:. However, it is very slow compared to most filters. Sigma values : For simplicity, you can set the 2 sigma values to be the same. A main part of our strategy will be to load each raw pixel once, and reuse it to calculate all pixels in the output filtered image that need this pixel value.

The math of the filter is that of the usual bilateral filter, except that the sigma color is calculated in the neighborhood, and clamped by the optional input value.

The call blur src, dst, ksize, anchor, borderType is equivalent to boxFilter src, dst, src. The function computes and returns the coordinate of a donor pixel corresponding to the specified extrapolated pixel when using the specified extrapolation border mode.

## Image mean filtering (i) â€“ in Python

Normally, the function is not called directly.I recently had to computationally alter some images, an ended up getting interested in some of the basic image manipulation techniques. The result is this post. For anyone thinking about doing serious image processing, they should be the first place to look. However, I am not planning on putting anything into production. Instead the goal of this post is to try and understand the fundamentals of a few simple image processing techniques.

Because of this, I am going to stick to using numpy to preform most of the manipulations, although I will use other libraries now and then. The first two indices represent the Y and X position of a pixel, and the third represents the RGB colour value of the pixel. Let's take a look at what the image is of. It is a photo of a painting of a dog.

The painting itself was found in a flat in London I lived in may years ago, abandoned by its previous owner. I don't know what the story behind it is. If you do, please get in touch. We can see that whichever bumbling fool took that photo of the painting also captured a lot of the wall.

We can crop the photo so we are only focused on the painting itself. In numpy, this is just a matter of slicing the image array. Each pixel of the image is represented by three integers: the RGB value of its colour. Splitting the image into seperate colour components is just a matter of pulling out the correct slice of the image array:.

When using matplotlib's imshow to display images, it is important to keep track of which data type you are using, as the colour mapping used is data type dependent: if a float is used, the values are mapped to the rangeso we need to cast to type "uint8" to get the expected behavior. A good discussion of this issue can be found here here. In my first edition of this post I made this mistake. Thanks to commenter Rusty Chris Holleman for pointing out the problem. Representing colour in this way, we can think of each pixel as a point in a three dimensional space.

Thinking of colour this way, we can apply various transformations to the colour "point". An interesting example of these is "rotating" the colour. There is some subtleties - a legal colours officially exist as integer points in a three dimensional cube of side lengths