Mean shift algorithm

docs/examples/image_segmentation/mean_shift.jl

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+# ---
+# cover: assets/meanshift.gif
+# title: Mean Shift Segmentation Algorithm
+# description: This demo shows how to use the meanshift algorithm to segment an image.
+# author: Ashwani Rathee
+# date: 2021-09-18
+# ---
+
+# Mean Shift segmentation is a local homogenization technique that is very useful
+# for damping shading or tonality differences in localized objects.
+# It replaces each pixel with the mean of the pixels in a range-r neighborhood 
+# and whose value is within a distance d.
+
+# K-means segmentation is another segmentation technique which is popular
+# but has two main issues:
+# -  We have specify a prior on the number of clusters(Number of K which is no of
+#    segments).
+# - It can be sensitive to value of k-means parameter.
+
+# Meanshift mitigates the above two issues.
+# Let's say below is the pixel feature distribution in an image when we take pixels
+# and we map it in feature map.
+
+# ![](assets/pixelf.png)
+
+# Below example image shows x,y coordinates corresponds to features and 3rd column 
+# is the density of the feature.
+
+# ![](assets/normalized.png)
+
+# - Each hill represents a cluster
+# - Peak(mode) of hill represents "center" of the cluster
+# - Each pixel climbs the steepest hill within its neighborhood
+# - Pixel assigned to the hill(cluster) it climbs. That's the idea behind meanshift. 
+# Those hills are then assigned labels and the image is segmented.
+
+# ![](assets/coloredpfd.png)
+
+# The Mean Shift takes usually 3 inputs:
+
+# - A distance function for measuring distances between pixels. Usually the 
+#   Euclidean distance, but any other well defined distance function could be used. 
+#   The Manhattan Distance is another useful choice sometimes.
+# - A radius. All pixels within this radius (measured according the above distance) 
+#   will be accounted for the calculation.
+# - A value difference. From all pixels inside radius r, we will take only those 
+#   whose values are within this difference for calculating the mean
+
+# ## Mean Shift Algorithm
+
+# Given: Distribution of N pixels in feature space.
+
+# Task: Find modes(clusters) of distribution. 
+
+# Clustering:
+# - Set $m_i = f_i$ as initial mean fro each pixel idea
+# - Repeat the following for each mean mi:
+#   - place window of size $w$ around $m_i$.
+#   - compute centroid m within the window set $mi = main$
+#   - stop if shift in mean $m_i$ is less than a threshoold $\epsilon$, $m_i$ is the mode
+
+# It's a very simple but computationally expensive method which doesn't require input of
+# the number of clusters. Very robust to outliers and clustering depends on window size w.
+
+using Images
+using ImageSegmentation, TestImages
+using IndirectArrays
+
+img = Gray.(testimage("blobs"))
+img = imresize(img, (128, 128));
+
+
+# Now let's segment images with mean shift clustering algorithm
+
+segments = meanshift(img, 16, 8/255) # parameters are smoothing radii: spatial=16, intensity-wise=8/255
+labels = labels_map(segments)
+colored_labels = IndirectArray(labels, distinguishable_colors(maximum(labels)))
+masked_colored_labels = colored_labels .* (1 .- img)
+
+mosaic(img, colored_labels, masked_colored_labels; nrow=1)
+
+# Here we use `IndirectArray` to store the indexed image, for more explaination on it please
+# check the tutorial [Indexed image in 5 minutes](@ref demo_indexed_image).
+
+# ## References:
+# - [Mean Shift Clustering](https://en.wikipedia.org/wiki/Mean_shift)
+# - http://vision.stanford.edu/teaching/cs131_fall1617/lectures/lecture13_kmeans_mean_shift_cs131_2016
+
+save("assets/meanshift.gif", cat(img, colored_labels, masked_colored_labels; dims=3); fps=1) #src