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‎README.md‎

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| [Emerging Hotspots](xrspatial/emerging_hotspots.py) | Classifies time-series hot/cold spot trends using Gi* and Mann-Kendall | ✅️ | ✅️ | ✅️ | ✅️ |
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| [Mean](xrspatial/focal.py) | Computes the mean value within a sliding neighborhood window | ✅️ | ✅️ | ✅️ | ✅️ |
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| [Focal Statistics](xrspatial/focal.py) | Computes summary statistics over a sliding neighborhood window | ✅️ | ✅️ | ✅️ | ✅️ |
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| [Bilateral](xrspatial/bilateral.py) | Feature-preserving smoothing via bilateral filtering | ✅️ | ✅️ | ✅️ | ✅️ |
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‎docs/source/reference/focal.rst‎

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xrspatial.focal.mean
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Bilateral
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=========
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.. autosummary::
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:toctree: _autosummary
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xrspatial.bilateral.bilateral
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Focal Statistics
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================

‎examples/user_guide/17_Bilateral_Filter.ipynb‎

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{
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"cells": [
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# Bilateral filtering\n",
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"\n",
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"The bilateral filter smooths a raster while preserving edges. Unlike a simple mean filter, it weights each neighbor by both spatial distance and value similarity. Pixels across a sharp boundary contribute very little, so edges stay sharp while flat areas get smoothed.\n",
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"\n",
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"Two parameters control the behavior:\n",
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"- **sigma_spatial**: how far the spatial Gaussian reaches (kernel radius = ceil(2 * sigma_spatial))\n",
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"- **sigma_range**: how much value difference is tolerated before a neighbor gets downweighted"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"import numpy as np\n",
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"import xarray as xr\n",
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"import matplotlib.pyplot as plt\n",
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"\n",
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"from xrspatial import bilateral\n",
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"from xrspatial import mean\n",
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"from xrspatial.terrain import generate_terrain"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Generate a synthetic terrain with noise\n",
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"\n",
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"We'll create a DEM, add Gaussian noise, and then compare bilateral filtering against the standard mean filter."
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"W, H = 600, 400\n",
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"cvs_terrain = xr.DataArray(\n",
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" np.zeros((H, W)),\n",
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" dims=['y', 'x'],\n",
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" coords={'y': np.linspace(0, 100, H), 'x': np.linspace(0, 150, W)},\n",
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")\n",
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"terrain = generate_terrain(cvs_terrain, seed=42)\n",
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"\n",
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"# Add noise\n",
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"rng = np.random.default_rng(123)\n",
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"noise = rng.normal(0, 15, terrain.shape)\n",
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"noisy_terrain = terrain.copy(data=terrain.values + noise)\n",
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"\n",
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"fig, axes = plt.subplots(1, 2, figsize=(14, 5))\n",
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"terrain.plot(ax=axes[0], cmap='terrain')\n",
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"axes[0].set_title('Clean terrain')\n",
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"noisy_terrain.plot(ax=axes[1], cmap='terrain')\n",
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"axes[1].set_title('Noisy terrain')\n",
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"plt.tight_layout()"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Compare bilateral vs. mean filter\n",
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"\n",
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"The mean filter blurs edges. The bilateral filter preserves them."
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"smoothed_bilateral = bilateral(noisy_terrain, sigma_spatial=2.0, sigma_range=20.0)\n",
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"smoothed_mean = mean(noisy_terrain, passes=3)\n",
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"\n",
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"fig, axes = plt.subplots(1, 3, figsize=(18, 5))\n",
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"\n",
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"noisy_terrain.plot(ax=axes[0], cmap='terrain')\n",
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"axes[0].set_title('Noisy input')\n",
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"\n",
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"smoothed_mean.plot(ax=axes[1], cmap='terrain')\n",
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"axes[1].set_title('Mean filter (3 passes)')\n",
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"\n",
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"smoothed_bilateral.plot(ax=axes[2], cmap='terrain')\n",
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"axes[2].set_title('Bilateral filter')\n",
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"\n",
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"plt.tight_layout()"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Effect of sigma_range\n",
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"\n",
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"Smaller `sigma_range` preserves more edges; larger values allow smoothing across bigger value differences."
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"sigma_ranges = [5.0, 20.0, 100.0]\n",
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"\n",
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"fig, axes = plt.subplots(1, len(sigma_ranges), figsize=(18, 5))\n",
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"for ax, sr in zip(axes, sigma_ranges):\n",
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" result = bilateral(noisy_terrain, sigma_spatial=2.0, sigma_range=sr)\n",
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" result.plot(ax=ax, cmap='terrain')\n",
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" ax.set_title(f'sigma_range = {sr}')\n",
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"plt.tight_layout()"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Step-edge preservation\n",
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"\n",
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"A clear demonstration: a raster with a sharp vertical edge. The bilateral filter keeps the boundary; the mean filter blurs it."
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"step = np.zeros((50, 100))\n",
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"step[:, 50:] = 100.0\n",
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"\n",
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"# Add a bit of noise\n",
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"step_noisy = step + rng.normal(0, 5, step.shape)\n",
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"step_agg = xr.DataArray(step_noisy, dims=['y', 'x'])\n",
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"\n",
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"step_bilateral = bilateral(step_agg, sigma_spatial=2.0, sigma_range=10.0)\n",
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"step_mean = mean(step_agg, passes=3)\n",
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"\n",
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"fig, axes = plt.subplots(1, 3, figsize=(15, 4))\n",
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"step_agg.plot(ax=axes[0], cmap='gray')\n",
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"axes[0].set_title('Noisy step edge')\n",
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"step_mean.plot(ax=axes[1], cmap='gray')\n",
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"axes[1].set_title('Mean filter')\n",
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"step_bilateral.plot(ax=axes[2], cmap='gray')\n",
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"axes[2].set_title('Bilateral filter')\n",
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"plt.tight_layout()\n",
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"\n",
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"# Cross-section\n",
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"row = 25\n",
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"fig, ax = plt.subplots(figsize=(10, 4))\n",
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"ax.plot(step_agg.data[row], label='Noisy', alpha=0.5)\n",
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"ax.plot(step_mean.data[row], label='Mean', linewidth=2)\n",
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"ax.plot(step_bilateral.data[row], label='Bilateral', linewidth=2)\n",
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"ax.legend()\n",
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"ax.set_xlabel('Column')\n",
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"ax.set_ylabel('Value')\n",
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"ax.set_title('Cross-section at row 25')\n",
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"plt.tight_layout()"
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]
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "Python 3",
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"language": "python",
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"name": "python3"
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},
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"language_info": {
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"name": "python",
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"version": "3.10.0"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 4
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}

‎xrspatial/__init__.py‎

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from xrspatial.aspect import aspect # noqa
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from xrspatial.balanced_allocation import balanced_allocation # noqa
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from xrspatial.bilateral import bilateral # noqa
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from xrspatial.bump import bump # noqa
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from xrspatial.corridor import least_cost_corridor # noqa
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from xrspatial.cost_distance import cost_distance # noqa

‎xrspatial/accessor.py‎

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from .focal import mean
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return mean(self._obj, **kwargs)
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def bilateral(self, **kwargs):
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from .bilateral import bilateral
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return bilateral(self._obj, **kwargs)
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# ---- Morphological ----
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def morph_erode(self, **kwargs):
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def bilateral(self, **kwargs):
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from .bilateral import bilateral
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return bilateral(self._obj, **kwargs)
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def morph_erode(self, **kwargs):

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