diff --git a/scripts/libraries/mtx.py b/scripts/libraries/mtx.py
new file mode 100644
index 000000000..e53fdda63
--- /dev/null
+++ b/scripts/libraries/mtx.py
@@ -0,0 +1,96 @@
+# The MIT License (MIT)
+#
+# Copyright (c) 2019 Nick Lee
+#
+# Permission is hereby granted, free of charge, to any person obtaining a copy of
+# this software and associated documentation files (the "Software"), to deal in
+# the Software without restriction, including without limitation the rights to
+# use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of
+# the Software, and to permit persons to whom the Software is furnished to do so,
+# subject to the following conditions:
+#
+# The above copyright notice and this permission notice shall be included in all
+# copies or substantial portions of the Software.
+#
+# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+# IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS
+# FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR
+# COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER
+# IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
+# CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
+
+def _dot(a, b):
+ s = 0
+ for i in range(0, len(b)):
+ s += a[i] * b[i]
+ return s
+
+def mul(A, b):
+ return [_dot(row, b) for row in A]
+
+def _height(A):
+ return len(A)
+
+def _width(A):
+ return len(A[0])
+
+def _max_magnitude_row(A, column):
+ first_row = column
+
+ max_row = first_row
+ max_value = A[first_row][column]
+
+ for i in range(first_row+1, _height(A)):
+ if abs(A[i][column]) > abs(max_value):
+ max_row = i
+ max_value = A[i][column]
+
+ return max_row
+
+def _subtract_rows_below(A, row, column, pivot_value):
+ # Fill in factors where entries will become zero.
+ for i in range(row+1, _height(A)):
+ A[i][column] /= pivot_value
+
+ for i in range(row+1, _height(A)):
+ for j in range(column+1, _width(A)):
+ A[i][j] -= (A[i][column] * A[row][j])
+
+def lu(A):
+ P = None
+ for pivot_column in range(0, _width(A)-1):
+ pivot_row = pivot_column
+ max_row = _max_magnitude_row(A, pivot_column)
+ pivot_value = A[max_row][pivot_column]
+
+ if max_row != pivot_row:
+ A[pivot_row], A[max_row] = A[max_row], A[pivot_row]
+
+ if P is None:
+ P = list(range(0, _height(A)))
+
+ P[pivot_row], P[max_row] = P[max_row], P[pivot_row]
+
+ _subtract_rows_below(A, pivot_row, pivot_column, pivot_value)
+ return P,A
+
+def _forward_substitute(A, b):
+ for i in range(1, len(b)):
+ for j in range(0, i):
+ b[i] = b[i] - (b[j] * A[i][j])
+
+def _backward_substitute(A, b):
+ size = len(b)
+ b[-1] = b[-1] / A[-1][-1]
+ for i in range(size-2, -1, -1):
+ for j in range(i+1, size):
+ b[i] = b[i] - (b[j] * A[i][j])
+ b[i] = b[i] / A[i][i]
+
+def solve(PLU, b):
+ P, LU = PLU
+
+ x = b[:] if P is None else [b[i] for i in P] # permutation
+ _forward_substitute(LU, x)
+ _backward_substitute(LU, x)
+ return x
diff --git a/scripts/libraries/rv/LICENSE.txt b/scripts/libraries/rv/LICENSE.txt
new file mode 100644
index 000000000..f288702d2
--- /dev/null
+++ b/scripts/libraries/rv/LICENSE.txt
@@ -0,0 +1,674 @@
+ GNU GENERAL PUBLIC LICENSE
+ Version 3, 29 June 2007
+
+ Copyright (C) 2007 Free Software Foundation, Inc.
+ Everyone is permitted to copy and distribute verbatim copies
+ of this license document, but changing it is not allowed.
+
+ Preamble
+
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+
+ The licenses for most software and other practical works are designed
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+share and change all versions of a program--to make sure it remains free
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+GNU General Public License for most of our software; it applies also to
+any other work released this way by its authors. You can apply it to
+your programs, too.
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+
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+free software which everyone can redistribute and change under these terms.
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+to attach them to the start of each source file to most effectively
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+ (at your option) any later version.
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+ but WITHOUT ANY WARRANTY; without even the implied warranty of
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+Also add information on how to contact you by electronic and paper mail.
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+ If the program does terminal interaction, make it output a short
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+ You should also get your employer (if you work as a programmer) or school,
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+.
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+.
diff --git a/scripts/libraries/rv/README.md b/scripts/libraries/rv/README.md
new file mode 100644
index 000000000..e96cbd386
--- /dev/null
+++ b/scripts/libraries/rv/README.md
@@ -0,0 +1,173 @@
+# OpenRV - Robot Vision routines for OpenMV
+
+[OpenMV](https://openmv.io) is a small camera board for machine vision. I use it
+to direct my robot. [The software
+library](http://docs.openmv.io/library/index.html) is adequate, but lacks some
+algorithms I need. Out comes this project, in which I implement a few missing
+pieces myself. I hope it could save time for someone who tries to do the same.
+
+**Everything is tested on OpenMV Cam H7**
+
+## Prerequisites
+
+Vector and matrix are mainstay in machine vision. Finding no satisfactory
+libraries, I have again implemented my own.
+
+#### Vector Operations on MicroPython
+
+- [Project](https://gitlab.com/nickoala/micropython-vec)
+- [Package](https://pypi.org/project/micropython-vec/)
+
+#### Fast Matrix Multiplication and Linear Solver on MicroPython
+
+- [Project](https://gitlab.com/nickoala/micropython-mtx)
+- [Package](https://pypi.org/project/micropython-mtx/)
+
+Along with this project's `rv` package, the OpenMV camera's SD card should
+contain:
+
+```
+/
+├── mtx.py
+├── rv
+│ ├── __init__.py
+│ ├── moments.py
+│ ├── planar.py
+│ └── quickshiftpp.py
+└── vec
+ ├── distance.py
+ └── __init__.py
+```
+
+**In addition, you need some theoretical backgrounds to use vision algorithms
+effectively. This page does not give you those backgrounds. Study them
+yourself.**
+
+## Hu moments
+
+[Hu moments](https://docs.opencv.org/2.4/modules/imgproc/doc/structural_analysis_and_shape_descriptors.html#humoments)
+[is a shape descriptor](https://www.pyimagesearch.com/2014/10/27/opencv-shape-descriptor-hu-moments-example/)
+[invariant to translation, scale, and rotation](https://www.learnopencv.com/shape-matching-using-hu-moments-c-python/).
+That means it can recognize the same shape no matter its location, size, and orientation in the picture.
+
+#### Usage
+
+The last element of Hu moments is somewhat of an oddball. It indicates
+reflection rather than the general shape. For matching, the last element should
+be dropped.
+
+Use the function `vec.distance.euclidean()` to see how close two vectors are.
+
+```python
+import rv.moments
+import vec.distance
+import image
+
+a = image.Image('/images/a.pgm')
+b = image.Image('/images/b.pgm')
+
+ha = rv.moments.hu(a)
+hb = rv.moments.hu(b)
+
+print(vec.distance.euclidean(ha[:-1], hb[:-1]))
+```
+
+**Remark:** Although accepting gray-level images, this implementation treats
+pixels as either 0 or 1. Pixels having a non-zero brightness are treated as 1.
+This speeds up calculation.
+
+**More:** [test_moments.py](test/test_moments.py)
+
+## Planar homography
+
+Map points from one coordinate system to another. For example, a red ball sits
+at (90, 50) on the image and you know it is on the floor (not floating in air),
+planar homography can map the image point (90, 50) to a position on the floor,
+telling you how far the red ball is in front of the robot and how much left or
+right. In this case, points are essentially mapped from the *image coordinate
+system* to the *floor coordinate system*.
+
+Once you can map points, finding out the size of objects is straight-forward.
+
+#### Usage
+
+It works only when two coordinate systems (i.e. the two planes) are fixed
+relative to each other. In other words, the camera's height and orientation
+relative to the floor cannot change.
+
+**[First, you have to calibrate for a homography matrix, which is a very long
+story. I have devoted an entire directory to discuss the process. Take a look
+there.](homography)**
+
+Once you have the matrix, the rest is easy.
+
+```python
+import rv.planar
+
+H = [[ 3.14916496e+01, -9.79038178e+02, 1.03951636e+05],
+ [ 7.57939015e+02, -3.31912533e+01, -5.86807545e+04],
+ [ 2.06572544e-01, 2.03579263e+00, 1.00000000e+00]]
+
+p = rv.planar.Planar(H)
+
+image_points = [[83, 109],
+ [70, 100],
+ [51, 92]]
+
+print(p.project(image_points))
+```
+
+**More:** [test_planar.py](test/test_planar.py)
+
+## Quickshift++
+
+[The latest member](https://github.com/google/quickshift) [of the
+Meanshift](http://www.chioka.in/meanshift-algorithm-for-the-rest-of-us-python/)
+[family of clustering
+algorithms](https://github.com/Nick-Ol/MedoidShift-and-QuickShift), Quickshift++
+accepts a bunch of points and group them. I use it to "discover" the colors of
+disks on the floor, before using colors to pick out the disks. This saves me
+from hard-coding the colors beforehand, and makes the robot adaptive.
+
+It is not optimized to handle a large number of points. OpenMV's limited memory
+precludes handling a lot of points anyway. Don't expect to use it to segment an
+entire image.
+
+#### Usage
+
+```python
+import rv.quickshiftpp
+
+points = [
+ # cluster 1
+ [1, 1],
+ [1.0, 1.2],
+ [0.9, 1.1],
+ [0.95, 0.99],
+
+ # cluster 2
+ [3.3, 3.0],
+
+ # cluster 3
+ [5.0, 8.2],
+ [5.5, 7.9],
+ [4.8, 8.1],
+ [5.1, 7.7],
+]
+
+print(rv.quickshiftpp.cluster(points,
+ k=2,
+ beta=0.2))
+```
+
+The parameter `k` determines how density is estimated. It uses *distance to the
+k-th nearest neighbor* to estimate density around each point.
+
+The parameter `beta` determines how much density is allowed to vary within
+cluster cores. Here is not the place to explain what "cluster core" means. Some
+theoretical understanding cannot be avoided.
+
+In short, use `k` and `beta` to tune the clustering.
+
+**More:** [test_quickshiftpp.py](test/test_quickshiftpp.py) and
+ [test_quickshiftpp_colors.py](test/test_quickshiftpp_colors.py)
diff --git a/scripts/libraries/rv/__init__.py b/scripts/libraries/rv/__init__.py
new file mode 100644
index 000000000..8b1378917
--- /dev/null
+++ b/scripts/libraries/rv/__init__.py
@@ -0,0 +1 @@
+
diff --git a/scripts/libraries/rv/moments.py b/scripts/libraries/rv/moments.py
new file mode 100644
index 000000000..8c8dd6db8
--- /dev/null
+++ b/scripts/libraries/rv/moments.py
@@ -0,0 +1,86 @@
+import math
+
+def _sum(img, roi, f):
+ x, y, w, h = roi or (0, 0, img.width(), img.height())
+ s = 0
+ for i in range(x, x + w):
+ for j in range(y, y + h):
+ if img.get_pixel(i,j) != 0:
+ s += f(i, j)
+ return s
+
+def centroid(img, roi=None, return_intermediate=False):
+ m10 = _sum(img, roi, lambda x,y: x)
+ m01 = _sum(img, roi, lambda x,y: y)
+ m00 = _sum(img, roi, lambda x,y: 1)
+
+ c = [0, 0] if m00 == 0 else [float(m10 / m00), float(m01 / m00)]
+
+ return [m00, c] if return_intermediate else c
+
+def central(img, roi=None, return_intermediate=False):
+ results = centroid(img, roi, return_intermediate=True)
+ cx, cy = results[-1]
+
+ u20 = _sum(img, roi, lambda x,y: (x-cx)**2)
+ u11 = _sum(img, roi, lambda x,y: (x-cx) * (y-cy))
+ u02 = _sum(img, roi, lambda x,y: (y-cy)**2)
+
+ u30 = _sum(img, roi, lambda x,y: (x-cx)**3)
+ u21 = _sum(img, roi, lambda x,y: (x-cx)**2 * (y-cy))
+ u12 = _sum(img, roi, lambda x,y: (x-cx) * (y-cy)**2)
+ u03 = _sum(img, roi, lambda x,y: (y-cy)**3)
+
+ us = [u20, u11, u02, u30, u21, u12, u03]
+
+ return (results + [us]) if return_intermediate else us
+
+def normalized_central(img, roi=None, return_intermediate=False):
+ results = central(img, roi, return_intermediate=True)
+ m00, _, [u20, u11, u02, u30, u21, u12, u03] = results
+
+ if m00 == 0:
+ ns = [0, 0, 0, 0, 0, 0, 0]
+ else:
+ m2 = m00**2
+ m3 = m00**2.5
+ n20, n11, n02 = u20/m2, u11/m2, u02/m2
+ n30, n21, n12, n03 = u30/m3, u21/m3, u12/m3, u03/m3
+
+ ns = [n20, n11, n02, n30, n21, n12, n03]
+
+ return (results + [ns]) if return_intermediate else ns
+
+def hu(img, roi=None, return_intermediate=False):
+ results = normalized_central(img, roi, return_intermediate=True)
+ n20, n11, n02, n30, n21, n12, n03 = results[-1]
+
+ h0 = n20 + n02
+
+ h1 = (n20 - n02)**2 + 4 * n11 * n11
+
+ _n30_3n12 = n30 - 3 * n12
+ _3n21_n03 = 3 * n21 - n03
+
+ h2 = _n30_3n12**2 + _3n21_n03**2
+
+ n3012 = n30 + n12
+ n3012_2 = n3012 * n3012
+
+ n2103 = n21 + n03
+ n2103_2 = n2103 * n2103
+
+ h3 = n3012_2 + n2103_2
+
+ h4 = (_n30_3n12 * n3012 * ( n3012_2 - 3 * n2103_2 )
+ + _3n21_n03 * n2103 * ( 3 * n3012_2 - n2103_2 ))
+
+ h5 = ( n20 - n02 ) * ( n3012_2 - n2103_2 ) + 4 * n11 * n3012 * n2103
+
+ h6 = (_3n21_n03 * n2103 * ( 3 * n3012_2 - n2103_2 )
+ - _n30_3n12 * n2103 * ( 3 * n3012_2 - n2103_2 ))
+
+ hs = [0 if h == 0 else math.copysign(math.log10(math.fabs(h)), h)
+ for h in [h0, h1, h2, h3, h4, h5, h6]]
+
+ return (results + [hs]) if return_intermediate else hs
diff --git a/scripts/libraries/rv/planar.py b/scripts/libraries/rv/planar.py
new file mode 100644
index 000000000..f5bcc639c
--- /dev/null
+++ b/scripts/libraries/rv/planar.py
@@ -0,0 +1,20 @@
+import mtx, vec
+
+class Planar(object):
+ def __init__(self, H, offset=[0,0]):
+ self.H = H
+ self.H_ = None # LU factorization of H
+ self.offset = offset
+
+ def project(self, points, reverse=False):
+ if reverse:
+ if self.H_ is None:
+ self.H_ = mtx.lu([r[:] for r in self.H])
+
+ qs = [mtx.solve(self.H_,
+ vec.sub(p, self.offset)+[1]) for p in points]
+ return [vec.div(q[:-1], q[-1]) for q in qs]
+ else:
+ qs = [mtx.mul(self.H, p+[1]) for p in points]
+ return [vec.add(self.offset,
+ vec.div(q[:-1], q[-1])) for q in qs]
diff --git a/scripts/libraries/rv/quickshiftpp.py b/scripts/libraries/rv/quickshiftpp.py
new file mode 100644
index 000000000..b373f5d64
--- /dev/null
+++ b/scripts/libraries/rv/quickshiftpp.py
@@ -0,0 +1,162 @@
+import vec.distance
+
+def distance_to_kth_nearest_neighbor(points, i, k):
+ fix = points[i]
+ d = [vec.distance.euclidean(fix, p) for p in points]
+ d.sort()
+ return d[k]
+ # Smallest distance is always to the point itself.
+ # First element can be ignored.
+ # Distance to k-th nearest neighbor is at index == k.
+
+def calculate_threshold(r, d, beta):
+ return r / (1 - beta)**(1 / d)
+
+def find_threshold_position(threshold, ascending):
+ lower = 0
+ upper = len(ascending) - 1
+
+ if ascending[upper][0] <= threshold:
+ return upper
+
+ # binary search
+ while upper - lower > 1:
+ i = (upper + lower) // 2
+ r = ascending[i][0]
+
+ if r == threshold:
+ # push `i` to last element equal to threshold
+ while i+1 < len(ascending) and ascending[i+1][0] == threshold:
+ i += 1
+ return i
+ elif r < threshold:
+ lower = i
+ else:
+ upper = i
+
+ if ascending[upper][0] <= threshold:
+ return upper
+ else:
+ return lower
+
+def in_which(x, sets):
+ for s in sets:
+ if x in s:
+ return s
+ return None
+
+def form_cluster_core(core_set,
+ existing_cores,
+ points,
+ sorted_radii,
+ seed_position,
+ threshold_position):
+
+ def include(current_position):
+ current_radius, current_index = sorted_radii[current_position]
+
+ core_set.add(current_index)
+
+ for other_position in range(0, threshold_position + 1):
+ other_radius, other_index = sorted_radii[other_position]
+
+ if other_index == current_index or other_index in core_set:
+ continue
+
+ distance = vec.distance.euclidean(
+ points[current_index], points[other_index])
+
+ if distance <= min(current_radius, other_radius):
+ # Connect current point to the other point
+
+ if in_which(other_index, existing_cores) is not None:
+ # The other point is already in another core.
+ # Current set will not be disjoint from existing cores.
+ # Current set cannot form a new core.
+ return False
+ else:
+ # Continue making connections, starting from new point.
+ clean = include(other_position)
+ if not clean:
+ return False
+ return True
+
+ return include(seed_position)
+
+def assign_cluster(clusters,
+ points,
+ sorted_radii,
+ position):
+
+ def find_cluster_to_belong(current_position):
+ _, current_index = sorted_radii[current_position]
+
+ cluster_set = in_which(current_index, clusters)
+ if cluster_set is not None:
+ # already belong to a cluster
+ return cluster_set
+
+ nearest_neighbor_distance = None
+ nearest_neighbor_position = None
+
+ # find nearest neighbor
+ for i in range(0, current_position):
+ _, other_index = sorted_radii[i]
+
+ distance = vec.distance.euclidean(
+ points[current_index], points[other_index])
+
+ if nearest_neighbor_distance is None \
+ or distance < nearest_neighbor_distance:
+ nearest_neighbor_distance = distance
+ nearest_neighbor_position = i
+
+ # join nearest neighbor's cluster
+ cluster_set = find_cluster_to_belong(nearest_neighbor_position)
+ cluster_set.add(current_index)
+ return cluster_set
+
+ find_cluster_to_belong(position)
+
+def cluster(points,
+ k,
+ beta,
+ return_modes=False):
+ dimension = len(points[0])
+
+ sorted_radii = [(distance_to_kth_nearest_neighbor(points, i, k=k), i)
+ for i in range(0, len(points))]
+ sorted_radii.sort()
+ # smallest radius first, i.e. highest density first.
+
+ modes = []
+ clusters = []
+ proposed_core = set()
+
+ for position in range(0, len(sorted_radii)):
+ radius, index = sorted_radii[position]
+
+ threshold = calculate_threshold(radius, dimension, beta)
+ threshold_position = find_threshold_position(threshold, sorted_radii)
+
+ if form_cluster_core(proposed_core,
+ clusters,
+ points,
+ sorted_radii,
+ seed_position=position,
+ threshold_position=threshold_position):
+ clusters.append(proposed_core)
+ proposed_core = set()
+
+ if return_modes:
+ modes.append(index)
+ else:
+ proposed_core.clear()
+
+ for position in range(0, len(sorted_radii)):
+ assign_cluster(clusters,
+ points,
+ sorted_radii,
+ position=position)
+
+ return (clusters, modes) if return_modes else clusters
diff --git a/scripts/libraries/vec/LICENSE.md b/scripts/libraries/vec/LICENSE.md
new file mode 100644
index 000000000..88e3dffbd
--- /dev/null
+++ b/scripts/libraries/vec/LICENSE.md
@@ -0,0 +1,20 @@
+The MIT License (MIT)
+
+Copyright (c) 2019 Nick Lee
+
+Permission is hereby granted, free of charge, to any person obtaining a copy of
+this software and associated documentation files (the "Software"), to deal in
+the Software without restriction, including without limitation the rights to
+use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of
+the Software, and to permit persons to whom the Software is furnished to do so,
+subject to the following conditions:
+
+The above copyright notice and this permission notice shall be included in all
+copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS
+FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR
+COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER
+IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
+CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
diff --git a/scripts/libraries/vec/README.md b/scripts/libraries/vec/README.md
new file mode 100644
index 000000000..3a1136913
--- /dev/null
+++ b/scripts/libraries/vec/README.md
@@ -0,0 +1,28 @@
+# Vector Operations on MicroPython
+
+Nothing fancy. Treating list as vector, this library performs common
+operations. I personally use it on [OpenMV](https://openmv.io) for robot vision.
+
+```python
+import vec
+
+a = [1, 2, 3]
+b = [4, 5, 6]
+
+vec.add(a, b) # [5, 7, 9]
+vec.sub(a, b) # [-3, -3, -3]
+vec.dot(a, b) # 32
+
+vec.mul(a, 2) # [2, 4, 6]
+vec.div(a, 2) # [0.5, 1.0, 1.5]
+```
+
+```python
+import vec.distance
+
+a = [2, 3]
+b = [5, 7]
+
+vec.distance.manhattan(a, b) # 7
+vec.distance.euclidean(a, b) # 5
+```
diff --git a/scripts/libraries/vec/__init__.py b/scripts/libraries/vec/__init__.py
new file mode 100644
index 000000000..45ca5b380
--- /dev/null
+++ b/scripts/libraries/vec/__init__.py
@@ -0,0 +1,17 @@
+def add(a, b):
+ return [a[i] + b[i] for i in range(0, min(len(a), len(b)))]
+
+def sub(a, b):
+ return [a[i] - b[i] for i in range(0, min(len(a), len(b)))]
+
+def mul(a, n):
+ return [a[i] * n for i in range(0, len(a))]
+
+def div(a, n):
+ return [a[i] / n for i in range(0, len(a))]
+
+def dot(a, b):
+ s = 0
+ for i in range(0, min(len(a), len(b))):
+ s += a[i] * b[i]
+ return s
diff --git a/scripts/libraries/vec/distance.py b/scripts/libraries/vec/distance.py
new file mode 100644
index 000000000..7042a369e
--- /dev/null
+++ b/scripts/libraries/vec/distance.py
@@ -0,0 +1,13 @@
+import math
+
+def manhattan(a, b):
+ s = 0
+ for i in range(0, min(len(a), len(b))):
+ s += abs(a[i] - b[i])
+ return s
+
+def euclidean(a, b):
+ s = 0
+ for i in range(0, min(len(a), len(b))):
+ s += (a[i] - b[i])**2
+ return math.sqrt(s)