crystal_map visualization discussion

[argerlt]

I've spent some time over the past few weeks working on this with limited success. Raising an issue here in hopes that some other people can weigh in with alternatives or advice.

Short version

orix.CrystalMap.plot is fast but restrictive. A mesh representation would be more ideal, but at the cost of some speed. I tried several methods, of which I listed the three best below with example code:

1) PatchCollection seems easiest to implement 2) if someone can figure out an irregular polygon version of 'pcolor', I think that would be faster, but it might not exist. 3) Plotly gives really powerful interactive plots, but without some direct JavaScript code, its prohibitively slow to set up.

The issue:

orix.CrystalMap currently plots EBSD images using matplotlib.pyplot.imshow. This is fast and intuitive, but has some drawbacks:

• it can only plot regular square grids.
• it requires the crystal_map.rotations to be in the form of a correctly ordered 2d array.
• while not necessary, it becomes more convenient to do flips or edits by flipping and/or transposing the 'crystal_map.rotations' variable. this can be problematic if the user is storing a lot of additional properties information.
• subsections like single grains or phases cut from the larger EBSD images are usually masks of the original. this can lead to memory overloads if, say, the user wanted 1000 crystalmap objects in a list, with one for each of 1000 grains in the CrystalMap.

The General solution:

EBSD maps should instead be plotted using some type of mesh tool. This is what MTEX does. For example, run the following MATLAB code, and pause the code in "generateUnitCells.m" (github link here)

clear all
close all
% load some dummy data
mtexdata alphaBetaTitanium
%plot it
plot(ebsd('Ti (alpha)'),ebsd('Ti (alpha)').orientations)

You can see that each "pixel" is really a copy of a polygon based on ebsd.unitCell with a transposed centroid. This has some important advantages:

• it can plot square, rectangular, and hex grids using the exact same method.
• crystal_map rotations can be 1d, 2d, 3d, or nd, and in whatever order the user chooses, as long as there is an equivalent of ebsd.prop.x and ebsd.prop.y with the correct centroids.
• plots can be easily rotated to weird angles and still look correct (super useful for my work aligning datasets, not sure how relevant for everyone else)
• There is a logical extension of this method to plotting irregular polygons. IE, plotting routines can be used for both pixels and grain maps.
• There is also a logical extension of this for 3d meshes. see plotly for some fun interactive examples

All that said, any mesh-based solution will inherently be slower than imshow. Thus, some considerable thought should be put into the best implementation.

Possible Implementation 1: Matplotlib PatchCollection

This seems like the closest parallel to what MTEX already does. I tried several methods and various implementations of jit, numba, multithreading, GPU acceleration, etc, but it seems the fastest method is the one used on the backend of hexbins

• define a single Polygon object that will be used for each pixel
• Pass the polygon into a PatchCollection with offsets=xy_centroids

Using dummy data, this looks a bit like this:

import numpy as np
from matplotlib.collections import PatchCollection, PolyCollection
from matplotlib.patches import RegularPolygon
import matplotlib.pyplot as plt
from matplotlib.cm import viridis
from matplotlib.transforms import AffineDeltaTransform as ADT
from matplotlib.transforms import Affine2D
import copy

# create a grid of centroids
spacing_1d = np.arange(1000, dtype=float)
xx, yy = np.meshgrid(spacing_1d, spacing_1d)
# square grid
sq_points = np.stack([xx.flatten(), yy.flatten()]).T
# hex grid
xx[::2, :] = xx[::2,:] +0.5
xx = xx*2/np.sqrt(3)
hex_points = np.stack([xx.flatten(), yy.flatten()]).T

# define unit polygons
single_sq_poly = RegularPolygon([0, 0], 4, radius=1**0.5, orientation=np.pi/4)
single_hex_poly = RegularPolygon([0, 0], 6, radius=1/np.sqrt(3), orientation=np.pi/3)
# make deep copies because plotting changes vector locations
sq_poly  = copy.deepcopy(single_sq_poly)
hex_poly  = copy.deepcopy(single_hex_poly)

# plot of single patches by themselves
fig, ax = plt.subplots(2, 2)
ax[0,0].set_xlim(-2, 2)
ax[0,0].set_ylim(-2, 2)
ax[0,0].set_aspect(1)
ax[0,0].add_patch(single_sq_poly)
ax[1,0].set_xlim(-2, 2)
ax[1,0].set_ylim(-2, 2)
ax[1,0].set_aspect(1)
ax[1,0].add_patch(single_hex_poly)

# define grid of patches
# create grids of patches
sq_grid = PatchCollection([sq_poly],offsets=sq_points,offset_transform=ADT(ax[0,1].transData))
hex_grid = PatchCollection([hex_poly],offsets=hex_points,offset_transform=ADT(ax[1,1].transData))

# these can be colored either by setting values;
sq_grid.set_array(np.random.rand(sq_points.size))

# or by defining rgb colors
c = viridis(np.random.randn(hex_points.size))
hex_grid.set_array(None)
hex_grid.set_color(c)

# plot of patch map
ax[0,1].set_xlim(-5, 205)
ax[0,1].set_ylim(-5, 205)
ax[0,1].set_aspect(1)
ax[0,1].add_collection(sq_grid)
#ax[0,1].scatter(sq_points[:,0],sq_points[:,1],)
ax[1,1].set_xlim(-5, 235)
ax[1,1].set_ylim(-5, 205)
ax[1,1].set_aspect(1)
ax[1,1].add_collection(hex_grid)

ax[0,0].set_title('single square patch')
ax[1,0].set_title('single hex patch')
ax[0,1].set_title('1000x1000 square intensity grid')
ax[1,1].set_title('1000x1000 hex rgb grid')
plt.tight_layout()

result looks like this, plots 2 million polygons in roughly 2-4 seconds (roughly comprable to MTEX)

The actual calculation is nearly instantaneous, it seems the holdup is in Matplotlib's plotting ability. Only real downside here is the plots are sluggish during zooming/panning, and adding tooltips will only slow this down further.

Possible Implementation 2: Plotting a triangle mesh using Matplotlib tripcolor

Here is a good demo of tripcolor in action and here is a snippet of code I wrote using it on the same dataset as above

import matplotlib.tri as tri
triang = tri.Triangulation(sq_points[:,0],sq_points[:,1])
fig,ax =plt.subplots(1)
ax.tripcolor(triang,np.random.rand(triang.triangles.shape[0]))

this seems to take much longer to calculate, but gives a more responsive plot. unfortunately, this ONLY works with TriMeshes (ie, meshes of triangles), which creates 2x as many faces for square grids and 6x for hex grids. This also means some additional book keeping has to be done.

There is also a quad mesh which seems to plot faster, but of course cannot do hexagonal plots. Also, these methods to not translate nicely to the concept of grain maps. (example of quad plot here)![https://matplotlib.org/stable/gallery/images_contours_and_fields/quadmesh_demo.html#sphx-glr-gallery-images-contours-and-fields-quadmesh-demo-py]

This FEELS like there should be a better way to make similar pcolor plots with irregular polygons, but I cannot figure it out. If someone else can, feel free to give it a go.

Possible Implementation 3: Plotly

For those who have not seen, you can do some incredibly cool interactive plots with plotly. In particular, an EBSD scan is essentially just what GIS people call a (Chloropleth, and plotly has some insanely fast tools for rendering them)[https://plotly.com/python/mapbox-county-choropleth/]

However, this has two downsides. 1) Plotly creates .html objects, which work well with Jupyter, not so well with Spyder or VS Code. 2) Plotly.py is, at its core, a bunch of code that writes JSON files which is then read by Plotly.js.

The first one seems acceptable, but the second one has been a problem. I can make super responsive 2000x2000 pixel ebsd plots and even 500x500x500 3d meshes, but writing them takes 5-10 minutes, because the python code is writing the data out as ASCII text. The fastest method I found was to build Mesh3D objects like this:

import plotly.graph_objects as go
from plotly.offline import plot

xx, yy = np.meshgrid(np.arange(400),np.arange(400))
x = xx.flatten()
y = yy.flatten()
points = np.stack([x,y]).T
width = xx.shape[0]
f_size = width*(width-1)
f1 = np.array([[i, i+1, i+width] for i in np.arange(f_size)], dtype=np.int64)
f1 = f1[(f1[:,0]+1)%400 !=0]
f2 = np.array([[i+width+1, i+1, i+width] for i in np.arange(f_size) ], dtype=np.int64)
f2 = f2[(f2[:,2]+1)%400 !=0]
faces = np.vstack([f1, f2])

m = go.Mesh3d(x=x,
              y=y,
              z = x*0,
              i=faces[:,0].tolist(), 
              j=faces[:,1].tolist(), 
              k=faces[:,2].tolist(),
              facecolor = cmap.viridis(x*np.pi%1),
              showscale=False
              )
# fig1 = go.Figure(data=m)
# plot(fig1, auto_open=True)

n = go.Mesh3d(x=x,
              y=y,
              z = x*0,
              i=[4,1],
              j=[1,4], 
              k=[0,5],
              facecolor = cmap.viridis(x*np.pi%1),
              showscale=False
              )
fig1 = go.Figure(data=m)
plot(fig1, auto_open=True)

Plots look like this. you get the tooltips for free, and can code in whatever information you want into them (rgb, euler angles, quaternion, axis-angle, etc)

Of course, this again brings up the problem of representing singular patches as multiple triangles.

I think there may be a more generic way to do this using Plotly.go.Scatter ,where each pixel is a different Scatter object. However, this shouldn't be done in Python because it is prohibitively slow to write out the necessary JSON. THAT SAID, if someone knowledgeable in JS has interest, this seems like a much better plotting tool for what we want.

Here is a very rough example for creating a50x50 grid.

import plotly.graph_objects as go
from plotly.offline import plot

spacing_1d = np.arange(50, dtype=float)
xx, yy = np.meshgrid(spacing_1d, spacing_1d)
x =xx.flatten()
y =yy.flatten()
ids = np.arange(50*50).reshape(50, 50)
con = np.stack(
    [ids[:-1, :-1].flatten(), ids[:-1, 1:].flatten(),
     ids[1:, 1:].flatten(), ids[1:, :-1].flatten(),
     ids[:-1, :-1].flatten()]).T

data= []
for i in np.arange(len(con)):
    c ='#%02x%02x%02x'%(np.random.randint(256),np.random.randint(256),np.random.randint(256))
    name = "I can put custom data here:{}".format(i)
    customdata = np.random.rand(3)
    data.append(
        go.Scatter(
            x=x[con[i]],
            y=y[con[i]],
            mode='lines',
            line=dict(color='rgb(150, 150, 150)', width=2),
            fillcolor=c,
            fill='toself',
            customdata=customdata,
            name= name,
            )
        )

fig = go.Figure(data)
fig.update_layout(width=1000, height=1000, showlegend=False,
                  template="none")

plot(fig, auto_open=True)

---

If anyone has any input, issues, feedback, etc, let me know.

[hakonanes]

You raise good points regarding the limitations of CrystalMap.plot(). It would be great if we could support alternatives alongside the current (basic) plotting!

Some questions and thoughts:

1. In what situations are your CrystalMap.rotations not in a nicely ordered 2D array? If you find working with this attribute too restrictive, we should improve it.
2. Plotting hundreds of crystal maps... We only considered in-memory data storage when implementing the class four years ago. @CSSFrancis has recently suggested supporting "lazy computation of crystal maps". You may have a common goal here.
3. I agree that it'd be better if crystal map data were structured in a grid of points rather than in cells. This would need a re-write of the class, but I'd open to it.
4. Before we add the possibility to do hex-grid plotting, we should support hexgonal grids in CrystalMap, I think.
5. The plotly plotting looks interesting. We could add plotly as an optional dependency and provide the plotting functionality in your point 3. as part of the plotting API.

[argerlt]

Thanks for reading this and giving feedback, this was helpful.

To preface my response, I am going to quote the MTEX page for Gridded EBSD Data because I think they hit the nail on the head:

By default MTEX ignores any gridding in the data. The reason for this is that when restricting to some subset, e.g. to a certain phase, the data will not form a regular grid anyway. For that reason, almost all functions in MTEX are implemented to work for arbitrarily aligned data.

On the other hand, there are certain functions that are only available ... for gridded data. Those functions include ... gradient computation and denoising.

(Omissions added for clarity, full quote at link)

At this stage, I'm not claiming we should make the default CrystalMap style ungridded like in MTEX, but I do think ONLY allowing gridded arrays is restrictive. Relying on a plotting method that only works on 2D arrays locks us into a singular choice, so this was about investigating plotting methods that could work in both cases.

To your points though @hakonanes :

In what situations are your CrystalMap.rotations not in a nicely ordered 2D array?

It's rare my data isn't on a square or hex grid, but like the quote from MTEX implies, I often want to look at and work on irregular subsections. An easy example is pulling out a handful of grains from a map of 3,000 to do a Parent Reconstruction, local cleanup, plotting, etc. Being able to pull out just the spots of interest via indexing (as done in MTEX) is super handy. It also makes problems easy to parallelize on a per-grain basis.

Plotting hundreds of crystal maps... We only considered in-memory data storage when implementing the class four years ago.

This wasn't the best demonstration by me. I was alluding to the fact that with an ungridded Map approach, you can pull out just subsections of interest to look at as opposed to relying on masking, which saves time and memory

I agree that it'd be better if crystal map data were structured in a grid of points rather than in cells. This would need a re-write of the class, but I'd open to it.

Neat! This is getting closer to what i actually want, but switching to a new method that cannot plot on day one seemed like a no-go, so I wanted to start with the plotting problem.

Before we add the possibility to do hex-grid plotting, we should support hexagonal grids in CrystalMap, I think.

This is a good point. I think the in-between might be to allow plotting any patch, but default to a square and add other defaults down the road.

The plotly plotting looks interesting. We could add plotly as an optional dependency and provide the plotting functionality in your point 3. as part of the plotting API.

I'm sort of cooling down on that option, I think it might be prohibitively slow to set up in Python. Leaving it here though in case someone else considers a similar approach, or figures out a way to improve what I did.

[hakonanes]

You seem to have thought about the structuring of crystallographic data a fair bit. Perhaps you can enlighten me as to what is meant by MTEX "ignoring gridding" in their EBSD class. Orientations, grid coordinates, and any auxiliary map properties are stored in flat arrays. When plotting, data is put into place based on the... grid coordinates? CrystalMap also stores data as flat arrays, but when plotting, data is put into place based on CrystalMap.shape. If I understand correctly, enforcing shape is really your issue?

Being able to pull out just the spots of interest via indexing (as done in MTEX) is super handy. It also makes problems easy to parallelize on a per-grain basis.

CrystalMap supports indexing in five different ways, as shown in this example. By "pulling out", you mean creating a new EBSD instance, or just getting the data? Could you show syntax?

as opposed to relying on masking, which saves time and memory

Yes, the current implementation in CrystalMap is arguably not the best... A (somehow) more restrictive but also more time and memory saving approach would be better.

I agree that it'd be better if crystal map data were structured in a grid of points rather than in cells. This would need a re-write of the class, but I'd open to it.

Quoting myself, I should qualify that I cannot lead such work at the moment, but I can assist!