# Would like to actually count the pixels of each color to see how that histogram turns out... from bokeh.models import ColumnDataSource, Div, LinearColorMapper, Slider from bokeh.plotting import column, curdoc, figure, row import colorcet from dataclasses import dataclass import datashader as ds import numpy as np import pandas as pd hows = ["linear", "log", "eq_hist", "eq_hist_new"] @dataclass(frozen=True) class Count: canvas_size: int agg: np.ndarray mask: np.ndarray unique_values: np.ndarray unique_counts: np.ndarray cdf: np.ndarray @dataclass class Transformed: how: str counts: np.ndarray agg: np.ndarray unique_values: np.ndarray def create_data(canvas_size): nsamples = 10000 rng = np.random.default_rng(1289242) dists = {cat: pd.DataFrame(dict([('x', rng.normal(x, s, nsamples)), ('y', rng.normal(y, s, nsamples)), ('val', val), ('cat', cat)])) for x, y, s, val, cat in [( 2, 2, 0.03, 10, "d1"), ( 2, -2, 0.10, 20, "d2"), ( -2, -2, 0.50, 30, "d3"), ( -2, 2, 1.00, 40, "d4"), ( 0, 0, 3.00, 50, "d5")] } df = pd.concat(dists, ignore_index=True) df["cat"]=df["cat"].astype("category") cvs = ds.Canvas(plot_width=canvas_size, plot_height=canvas_size) agg = cvs.points(source=df, x="x", y="y") agg = agg.data.ravel() mask = agg != 0 # Mask of non-zero values agg = agg[mask] # Only non-zero values unique_values, unique_counts = np.unique(agg, return_counts=True) # Unique values cdf = np.cumsum(unique_counts) / unique_counts.sum() return Count(canvas_size, agg, mask, unique_values, unique_counts, cdf) def process(how, count, eq_hist_new_power): # eq_hist_new_power only used if how == "eq_hist_new". counts = count.unique_counts if how == "linear": transformed_unique_values = count.unique_values.copy() transformed_agg = count.agg.copy() elif how == "log": transformed_unique_values = np.log1p(count.unique_values) transformed_agg = np.log1p(count.agg) elif how == "eq_hist": # Transform based on CDF cdf = count.cdf cdf = (cdf - cdf[0]) / (cdf[-1] - cdf[0]) # Normalised to range 0..1 transformed_unique_values = np.interp(count.unique_values, count.unique_values, cdf) transformed_agg = np.interp(count.agg, count.unique_values, cdf) elif how == "eq_hist_new": # Transform based on CDF counts = counts**eq_hist_new_power # Raise to power <= 1 cdf = np.cumsum(counts) cdf = (cdf - cdf[0]) / (cdf[-1] - cdf[0]) # Normalised to range 0..1 transformed_unique_values = np.interp(count.unique_values, count.unique_values, cdf) transformed_agg = np.interp(count.agg, count.unique_values, cdf) else: raise RuntimeError("Not implemented") return Transformed(how, counts, transformed_agg, transformed_unique_values) def shade(count, transformed, cmap): low = transformed.agg.min() high = transformed.agg.max() rspan, gspan, bspan = np.array(list(zip(*map(ds.colors.rgb, cmap)))) span = np.linspace(low, high, len(cmap)) r = np.interp(transformed.agg, span, rspan, left=255).astype(np.uint8) g = np.interp(transformed.agg, span, gspan, left=255).astype(np.uint8) b = np.interp(transformed.agg, span, bspan, left=255).astype(np.uint8) a = np.full_like(r, 255) rgba = np.column_stack([r, g, b, a]) canvas_size = count.canvas_size image = np.zeros((canvas_size*canvas_size), dtype=np.uint32) view = image.view(dtype=np.uint8).reshape((canvas_size*canvas_size, 4)) for i in range(4): view[count.mask, i] = rgba[:, i] image.shape = (canvas_size, canvas_size) return image count = None data_cds = {} image_cds = {} histogram_cds = {} data_color_mappers = {} histogram_color_mappers = {} def create_all_data(): global count count = create_data(canvas_size) for how in hows: transformed = process(how, count, eq_hist_new_power) image = shade(count, transformed, cmap) hist, edges = np.histogram(transformed.agg, bins=nbins) if how == "eq_hist_new": hist = hist**eq_hist_new_power data = dict(count=count.unique_values, transformed=transformed.unique_values, cdf=count.cdf) if how in data_cds: data_cds[how].data = data else: data_cds[how] = ColumnDataSource(data) data = dict(image=[image]) if how in image_cds: image_cds[how].data = data else: image_cds[how] = ColumnDataSource(data) data = dict(hist=hist, left=edges[:-1], right=edges[1:]) if how in histogram_cds: histogram_cds[how].data = data else: histogram_cds[how] = ColumnDataSource(data) def create_color_mappers(): for how in hows: low = data_cds[how].data["transformed"][0] high = data_cds[how].data["transformed"][-1] if how in data_color_mappers: data_color_mappers[how].low = low data_color_mappers[how].high = high else: data_color_mappers[how] = LinearColorMapper(palette=cmap, low=low, high=high) low = histogram_cds[how].data["left"][0] high = histogram_cds[how].data["left"][-1] if how in histogram_color_mappers: histogram_color_mappers[how].low = low histogram_color_mappers[how].high = high else: histogram_color_mappers[how] = LinearColorMapper(palette=cmap, low=low, high=high) nbins = 100 canvas_size = 200 cmap = colorcet.rainbow eq_hist_new_power = 0.5 h = 200 w = 350 lw = 2 # line width ms = 7 # marker size lc = "silver" # line color create_all_data() create_color_mappers() cols = [] for i, how in enumerate(hows): # Datashaded image. p0 = figure(width=w, height=w, title=f"how = '{how}'", toolbar_location=None) p0.x_range.range_padding = p0.y_range.range_padding = 0 p0.image_rgba(source=image_cds[how], image="image", x=0, y=0, dw=canvas_size, dh=canvas_size) # Transformed data space. p1 = figure(width=w, height=h, x_axis_label="Data space", y_axis_label="Transformed data space", title="Transform", toolbar_location=None) p1.line(source=data_cds[how], x="count", y="transformed", line_width=lw, color=lc) p1.scatter(source=data_cds[how], x="count", y="transformed", marker="o", size=ms, color=dict(field="transformed", transform=data_color_mappers[how])) # Linear histogram. p2 = figure(width=w, height=h, title="Linear histogram in transformed data space", x_axis_label="Transformed data space (= color space)", y_axis_label="Pixel counts", toolbar_location=None) p2.quad(source=histogram_cds[how], top="hist", bottom=0, left="left", right="right", color=dict(field="left", transform=histogram_color_mappers[how])) # Log histogram. p3 = figure(width=w, height=h, title="Log histogram in transformed data space", x_axis_label="Transformed data space (= color space)", y_axis_label="Pixel counts", y_axis_type="log", toolbar_location=None) p3.quad(source=histogram_cds[how], top="hist", bottom=1, left="left", right="right", color=dict(field="left", transform=histogram_color_mappers[how])) # CDF. p4 = figure(width=w, height=h, title="CDF in transformed data space", y_axis_label="CDF", x_axis_label="Transformed data space (= color space)", toolbar_location=None) p4.line(source=data_cds[how], x="transformed", y="cdf", line_width=lw, color=lc) p4.step(source=data_cds[how], x="transformed", y="cdf", line_width=lw, mode="after", color=lc) p4.scatter(source=data_cds[how], x="transformed", y="cdf", marker="o", size=ms, color=dict(field="transformed", transform=data_color_mappers[how])) col = column([p0, p1, p2, p3, p4]) cols.append(col) def power_callback(_attr, _old, new_value): global eq_hist_new_power eq_hist_new_power = new_value how = "eq_hist_new" transformed = process(how, count, eq_hist_new_power) data_cds[how].data = dict( count=count.unique_values, transformed=transformed.unique_values, cdf=count.cdf) image = shade(count, transformed, cmap) image_cds[how].data = dict(image=[image]) hist, edges = np.histogram(transformed.agg, bins=nbins) if how == "eq_hist_new": hist = hist**eq_hist_new_power histogram_cds[how].data = dict(hist=hist, left=edges[:-1], right=edges[1:]) def canvas_size_callback(_attr, _old, new_value): global canvas_size canvas_size = new_value create_all_data() create_color_mappers() # Colorbar column at end, just using an image. color_mapper = LinearColorMapper(palette=cmap, low=0, high=1) image = np.linspace(0.0, 1.0, len(cmap)) image = np.expand_dims(image, axis=0) p = figure(width=w, height=80, toolbar_location=None, x_range=(0, 1), y_range=(0, 1), title="Colormap") p.yaxis.visible = False p.grid.visible = False p.image(image=[image], color_mapper=color_mapper, x=0, y=0, dw=1, dh=1) power_slider = Slider(start=0.0, end=1.0, value=eq_hist_new_power, step=0.01, title="eq_hist_new power") power_slider.on_change("value", power_callback) canvas_size_slider = Slider(start=50, end=500, value=canvas_size, step=50, title="Canvas size") canvas_size_slider.on_change("value", canvas_size_callback) div = Div(text="

eq_hist_new raises the histogram bin counts to a power in the range " "0 <= power <= 1. This reduces the height of the larger counts with respect to the lower " "counts, bringing the histogram bins closer together where there were large gaps.

" "power=1 corresponds to the original eq_hist algorithm, power=0 makes all counts the same, " "power=0.5 takes square root of the counts.

", width=300) col = column([p, power_slider, canvas_size_slider, div]) cols.append(col) curdoc().add_root(row(cols))