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681 lines
23 KiB
Python
681 lines
23 KiB
Python
# -*- coding: utf-8 -*-
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"""
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Created on Thu Mar 1 11:20:35 2018
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@author: z5030440
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"""
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"""This script contains the functions needed for satellite derived shoreline (SDS) extraction"""
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# Initial settings
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import numpy as np
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import matplotlib.pyplot as plt
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import pdb
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import ee
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# other modules
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from osgeo import gdal, ogr, osr
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import tempfile
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from urllib.request import urlretrieve
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import zipfile
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# image processing modules
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import skimage.filters as filters
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import skimage.exposure as exposure
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import skimage.transform as transform
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import sklearn.decomposition as decomposition
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import skimage.measure as measure
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import skimage.morphology as morphology
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from sklearn.cluster import KMeans
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# import own modules
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from functions.utils import *
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# Download from ee server function
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def download_tif(image, polygon, bandsId):
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"""downloads tif image (region and bands) from the ee server and stores it in a temp file"""
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url = ee.data.makeDownloadUrl(ee.data.getDownloadId({
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'image': image.serialize(),
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'region': polygon,
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'bands': bandsId,
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'filePerBand': 'false',
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'name': 'data',
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}))
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local_zip, headers = urlretrieve(url)
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with zipfile.ZipFile(local_zip) as local_zipfile:
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return local_zipfile.extract('data.tif', tempfile.mkdtemp())
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def load_image(image, polygon, bandsId):
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"""
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Loads an ee.Image() as a np.array. e.Image() is retrieved from the EE database.
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The geographic area and bands to select can be specified
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KV WRL 2018
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Arguments:
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-----------
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image: ee.Image()
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image objec from the EE database
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polygon: list
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coordinates of the points creating a polygon. Each point is a list with 2 values
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bandsId: list
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bands to select, each band is a dictionnary in the list containing the following keys:
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crs, crs_transform, data_type and id. NOTE: you have to remove the key dimensions, otherwise
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the entire image is retrieved.
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Returns:
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-----------
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image_array : np.ndarray
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An array containing the image (2D if one band, otherwise 3D)
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georef : np.ndarray
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6 element vector containing the crs_parameters
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[X_ul_corner Xscale Xshear Y_ul_corner Yshear Yscale]
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"""
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local_tif_filename = download_tif(image, polygon, bandsId)
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dataset = gdal.Open(local_tif_filename, gdal.GA_ReadOnly)
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georef = np.array(dataset.GetGeoTransform())
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bands = [dataset.GetRasterBand(i + 1).ReadAsArray() for i in range(dataset.RasterCount)]
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return np.stack(bands, 2), georef
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def create_cloud_mask(im_qa, satname, plot_bool):
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"""
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Creates a cloud mask from the image containing the QA band information
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KV WRL 2018
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Arguments:
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-----------
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im_qa: np.ndarray
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Image containing the QA band
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satname: string
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short name for the satellite (L8, L7, S2)
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plot_bool: boolean
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True if plot is wanted
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Returns:
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-----------
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cloud_mask : np.ndarray of booleans
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A boolean array with True where the cloud are present
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"""
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# convert QA bits
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if satname == 'L8':
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cloud_values = [2800, 2804, 2808, 2812, 6896, 6900, 6904, 6908]
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elif satname == 'L7':
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cloud_values = [752, 756, 760, 764]
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cloud_mask = np.isin(im_qa, cloud_values)
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# remove isolated cloud pixels (there are some in the swash and they cause problems)
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if sum(sum(cloud_mask)) > 0:
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morphology.remove_small_objects(cloud_mask, min_size=10, connectivity=1, in_place=True)
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if plot_bool:
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plt.figure()
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plt.imshow(cloud_mask, cmap='gray')
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plt.draw()
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#cloud_shadow_values = [2976, 2980, 2984, 2988, 3008, 3012, 3016, 3020]
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#cloud_shadow_mask = np.isin(im_qa, cloud_shadow_values)
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return cloud_mask
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def read_eeimage(im, polygon, sat_name, plot_bool):
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"""
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Read an ee.Image() object and returns the panchromatic band, multispectral bands (B, G, R, NIR, SWIR)
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and a cloud mask. All outputs are at 15m resolution (bilinear interpolation for the multispectral bands)
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KV WRL 2018
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Arguments:
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-----------
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im: ee.Image()
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Image to read from the Google Earth Engine database
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plot_bool: boolean
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True if plot is wanted
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Returns:
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-----------
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im_pan: np.ndarray (2D)
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The panchromatic band (15m)
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im_ms: np.ndarray (3D)
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The multispectral bands interpolated at 15m
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im_cloud: np.ndarray (2D)
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The cloud mask at 15m
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crs_params: list
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EPSG code and affine transformation parameters
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"""
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im_dic = im.getInfo()
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# save metadata
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im_meta = im_dic.get('properties')
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meta = {'timestamp':im_meta['system:time_start'],
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'date_acquired':im_meta['DATE_ACQUIRED'],
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'geom_rmse_model':im_meta['GEOMETRIC_RMSE_MODEL'],
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'gcp_model':im_meta['GROUND_CONTROL_POINTS_MODEL'],
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'quality':im_meta['IMAGE_QUALITY_OLI'],
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'sun_azimuth':im_meta['SUN_AZIMUTH'],
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'sun_elevation':im_meta['SUN_ELEVATION']}
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im_bands = im_dic.get('bands')
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# delete dimensions key from dictionnary, otherwise the entire image is extracted
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for i in range(len(im_bands)): del im_bands[i]['dimensions']
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# load panchromatic band
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pan_band = [im_bands[7]]
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im_pan, crs_pan = load_image(im, polygon, pan_band)
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im_pan = im_pan[:,:,0]
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# load the multispectral bands (B2,B3,B4,B5,B6) = (blue,green,red,nir,swir1)
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ms_bands = [im_bands[1], im_bands[2], im_bands[3], im_bands[4], im_bands[5]]
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im_ms_30m, crs_ms = load_image(im, polygon, ms_bands)
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# create cloud mask
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qa_band = [im_bands[11]]
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im_qa, crs_qa = load_image(im, polygon, qa_band)
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im_qa = im_qa[:,:,0]
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im_cloud = create_cloud_mask(im_qa, sat_name, plot_bool)
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im_cloud = transform.resize(im_cloud, (im_pan.shape[0], im_pan.shape[1]),
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order=0, preserve_range=True, mode='constant').astype('bool_')
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# resize the image using bilinear interpolation (order 1)
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im_ms = transform.resize(im_ms_30m,(im_pan.shape[0], im_pan.shape[1]),
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order=1, preserve_range=True, mode='constant')
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# check if -inf values (means out of image) and add to cloud mask
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im_inf = np.isin(im_ms[:,:,0], -np.inf)
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im_nan = np.isnan(im_ms[:,:,0])
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im_cloud = np.logical_or(np.logical_or(im_cloud, im_inf), im_nan)
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# get the crs parameters for the image at 15m and 30m resolution
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crs = {'crs_15m':crs_pan, 'crs_30m':crs_ms, 'epsg_code':int(pan_band[0]['crs'][5:])}
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if plot_bool:
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# if there are -inf in the image, set them to 0 before plotting
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if sum(sum(np.isin(im_ms_30m[:,:,0], -np.inf).astype(int))) > 0:
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idx = np.isin(im_ms_30m[:,:,0], -np.inf)
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im_ms_30m[idx,0] = 0; im_ms_30m[idx,1] = 0; im_ms_30m[idx,2] = 0;
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im_ms_30m[idx,3] = 0; im_ms_30m[idx,4] = 0
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plt.figure()
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plt.subplot(221)
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plt.imshow(im_pan, cmap='gray')
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plt.title('PANCHROMATIC')
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plt.subplot(222)
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plt.imshow(im_ms_30m[:,:,[2,1,0]])
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plt.title('RGB')
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plt.subplot(223)
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plt.imshow(im_ms_30m[:,:,3], cmap='gray')
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plt.title('NIR')
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plt.subplot(224)
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plt.imshow(im_ms_30m[:,:,4], cmap='gray')
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plt.title('SWIR')
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plt.show()
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return im_pan, im_ms, im_cloud, crs, meta
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def rescale_image_intensity(im, cloud_mask, prob_high, plot_bool):
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"""
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Rescales the intensity of an image (multispectral or single band) by applying
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a cloud mask and clipping the prob_high upper percentile. This functions allows
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to stretch the contrast of an image.
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KV WRL 2018
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Arguments:
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-----------
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im: np.ndarray
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Image to rescale, can be 3D (multispectral) or 2D (single band)
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cloud_mask: np.ndarray
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2D cloud mask with True where cloud pixels are
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prob_high: float
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probability of exceedence used to calculate the upper percentile
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plot_bool: boolean
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True if plot is wanted
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Returns:
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-----------
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im_adj: np.ndarray
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The rescaled image
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"""
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prc_low = 0 # lower percentile
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vec_mask = cloud_mask.reshape(im.shape[0] * im.shape[1])
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if plot_bool:
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plt.figure()
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if len(im.shape) > 2:
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vec = im.reshape(im.shape[0] * im.shape[1], im.shape[2])
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vec_adj = np.ones((len(vec_mask), im.shape[2])) * np.nan
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for i in range(im.shape[2]):
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prc_high = np.percentile(vec[~vec_mask, i], prob_high)
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vec_rescaled = exposure.rescale_intensity(vec[~vec_mask, i], in_range=(prc_low, prc_high))
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vec_adj[~vec_mask,i] = vec_rescaled
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if plot_bool:
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plt.subplot(np.floor(im.shape[2]/2) + 1, np.floor(im.shape[2]/2), i+1)
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plt.hist(vec[~vec_mask, i], bins=200, label='original')
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plt.hist(vec_rescaled, bins=200, alpha=0.5, label='rescaled')
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plt.legend()
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plt.title('Band' + str(i+1))
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plt.show()
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im_adj = vec_adj.reshape(im.shape[0], im.shape[1], im.shape[2])
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if plot_bool:
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plt.figure()
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ax1 = plt.subplot(121)
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plt.imshow(im[:,:,[2,1,0]])
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plt.axis('off')
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plt.title('Original')
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ax2 = plt.subplot(122, sharex=ax1, sharey=ax1)
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plt.imshow(im_adj[:,:,[2,1,0]])
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plt.axis('off')
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plt.title('Rescaled')
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plt.show()
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else:
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vec = im.reshape(im.shape[0] * im.shape[1])
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vec_adj = np.ones(len(vec_mask)) * np.nan
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prc_high = np.percentile(vec[~vec_mask], prob_high)
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vec_rescaled = exposure.rescale_intensity(vec[~vec_mask], in_range=(prc_low, prc_high))
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vec_adj[~vec_mask] = vec_rescaled
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if plot_bool:
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plt.hist(vec[~vec_mask], bins=200, label='original')
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plt.hist(vec_rescaled, bins=200, alpha=0.5, label='rescaled')
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plt.legend()
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plt.title('Single band')
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plt.show()
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im_adj = vec_adj.reshape(im.shape[0], im.shape[1])
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if plot_bool:
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plt.figure()
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ax1 = plt.subplot(121)
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plt.imshow(im, cmap='gray')
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plt.axis('off')
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plt.title('Original')
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ax2 = plt.subplot(122, sharex=ax1, sharey=ax1)
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plt.imshow(im_adj, cmap='gray')
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plt.axis('off')
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plt.title('Rescaled')
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plt.show()
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return im_adj
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def hist_match(source, template):
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"""
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Adjust the pixel values of a grayscale image such that its histogram
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matches that of a target image
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Arguments:
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-----------
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source: np.ndarray
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Image to transform; the histogram is computed over the flattened
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array
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template: np.ndarray
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Template image; can have different dimensions to source
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Returns:
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-----------
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matched: np.ndarray
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The transformed output image
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"""
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oldshape = source.shape
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source = source.ravel()
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template = template.ravel()
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# get the set of unique pixel values and their corresponding indices and
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# counts
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s_values, bin_idx, s_counts = np.unique(source, return_inverse=True,
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return_counts=True)
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t_values, t_counts = np.unique(template, return_counts=True)
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# take the cumsum of the counts and normalize by the number of pixels to
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# get the empirical cumulative distribution functions for the source and
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# template images (maps pixel value --> quantile)
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s_quantiles = np.cumsum(s_counts).astype(np.float64)
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s_quantiles /= s_quantiles[-1]
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t_quantiles = np.cumsum(t_counts).astype(np.float64)
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t_quantiles /= t_quantiles[-1]
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# interpolate linearly to find the pixel values in the template image
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# that correspond most closely to the quantiles in the source image
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interp_t_values = np.interp(s_quantiles, t_quantiles, t_values)
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return interp_t_values[bin_idx].reshape(oldshape)
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def pansharpen(im_ms, im_pan, cloud_mask, plot_bool):
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"""
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Pansharpens a multispectral image (3D), using the panchromatic band (2D)
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and a cloud mask
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KV WRL 2018
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Arguments:
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-----------
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im_ms: np.ndarray
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Multispectral image to pansharpen (3D)
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im_pan: np.ndarray
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Panchromatic band (2D)
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cloud_mask: np.ndarray
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2D cloud mask with True where cloud pixels are
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plot_bool: boolean
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True if plot is wanted
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Returns:
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-----------
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im_ms_ps: np.ndarray
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Pansharpened multisoectral image (3D)
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"""
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# reshape image into vector and apply cloud mask
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vec = im_ms.reshape(im_ms.shape[0] * im_ms.shape[1], im_ms.shape[2])
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vec_mask = cloud_mask.reshape(im_ms.shape[0] * im_ms.shape[1])
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vec = vec[~vec_mask, :]
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# apply PCA to RGB bands
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pca = decomposition.PCA()
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vec_pcs = pca.fit_transform(vec)
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# replace 1st PC with pan band (after matching histograms)
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vec_pan = im_pan.reshape(im_pan.shape[0] * im_pan.shape[1])
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vec_pan = vec_pan[~vec_mask]
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vec_pcs[:,0] = hist_match(vec_pan, vec_pcs[:,0])
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vec_ms_ps = pca.inverse_transform(vec_pcs)
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# normalise between 0 and 1
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for i in range(vec_pcs.shape[1]):
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vec_ms_ps[:,i] = np.divide(vec_ms_ps[:,i] - np.min(vec_ms_ps[:,i]),
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np.max(vec_ms_ps[:,i]) - np.min(vec_ms_ps[:,i]))
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# reshape vector into image
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vec_ms_ps_full = np.ones((len(vec_mask), im_ms.shape[2])) * np.nan
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vec_ms_ps_full[~vec_mask,:] = vec_ms_ps
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im_ms_ps = vec_ms_ps_full.reshape(im_ms.shape[0], im_ms.shape[1], im_ms.shape[2])
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if plot_bool:
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plt.figure()
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ax1 = plt.subplot(121)
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plt.imshow(im_ms[:,:,[2,1,0]])
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plt.axis('off')
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plt.title('Original')
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ax2 = plt.subplot(122, sharex=ax1, sharey=ax1)
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plt.imshow(im_ms_ps[:,:,[2,1,0]])
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plt.axis('off')
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plt.title('Pansharpened')
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plt.show()
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return im_ms_ps
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def nd_index(im1, im2, cloud_mask, plot_bool):
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"""
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Computes normalised difference index on 2 images (2D), given a cloud mask (2D)
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KV WRL 2018
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Arguments:
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-----------
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im1, im2: np.ndarray
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Images (2D) with which to calculate the ND index
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cloud_mask: np.ndarray
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2D cloud mask with True where cloud pixels are
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plot_bool: boolean
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True if plot is wanted
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Returns: -----------
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im_nd: np.ndarray
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Image (2D) containing the ND index
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"""
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vec_mask = cloud_mask.reshape(im1.shape[0] * im1.shape[1])
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vec_nd = np.ones(len(vec_mask)) * np.nan
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vec1 = im1.reshape(im1.shape[0] * im1.shape[1])
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vec2 = im2.reshape(im2.shape[0] * im2.shape[1])
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temp = np.divide(vec1[~vec_mask] - vec2[~vec_mask],
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vec1[~vec_mask] + vec2[~vec_mask])
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vec_nd[~vec_mask] = temp
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im_nd = vec_nd.reshape(im1.shape[0], im1.shape[1])
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if plot_bool:
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plt.figure()
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plt.imshow(im_nd, cmap='seismic')
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plt.colorbar()
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plt.title('Normalised index')
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plt.show()
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return im_nd
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def find_wl_contours(im_ndwi, cloud_mask, min_contour_points, plot_bool):
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"""
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Computes normalised difference index on 2 images (2D), given a cloud mask (2D)
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KV WRL 2018
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Arguments:
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-----------
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im_ndwi: np.ndarray
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Image (2D) with the NDWI (water index)
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cloud_mask: np.ndarray
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2D cloud mask with True where cloud pixels are
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min_contour_points: int
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minimum number of points in each contour line
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plot_bool: boolean
|
|
True if plot is wanted
|
|
|
|
Returns: -----------
|
|
contours_wl: list of np.arrays
|
|
contains the (row,column) coordinates of the contour lines
|
|
|
|
"""
|
|
|
|
# reshape image to vector
|
|
vec_ndwi = im_ndwi.reshape(im_ndwi.shape[0] * im_ndwi.shape[1])
|
|
vec_mask = cloud_mask.reshape(cloud_mask.shape[0] * cloud_mask.shape[1])
|
|
vec = vec_ndwi[~vec_mask]
|
|
# apply otsu's threshold
|
|
t_otsu = filters.threshold_otsu(vec)
|
|
# use Marching Squares algorithm to detect contours on ndwi image
|
|
contours = measure.find_contours(im_ndwi, t_otsu)
|
|
# filter water lines
|
|
contours_wl = []
|
|
for i, contour in enumerate(contours):
|
|
# remove contour points that are around clouds (nan values)
|
|
if np.any(np.isnan(contour)):
|
|
index_nan = np.where(np.isnan(contour))[0]
|
|
contour = np.delete(contour, index_nan, axis=0)
|
|
# remove contours that have only few points (less than min_contour_points)
|
|
if contour.shape[0] > min_contour_points:
|
|
contours_wl.append(contour)
|
|
|
|
if plot_bool:
|
|
# plot otsu's histogram segmentation
|
|
plt.figure()
|
|
vals = plt.hist(vec, bins=200)
|
|
plt.plot([t_otsu, t_otsu],[0, np.max(vals[0])], 'r-', label='Otsu threshold')
|
|
plt.legend()
|
|
plt.show()
|
|
|
|
# plot the water line contours on top of water index
|
|
plt.figure()
|
|
plt.imshow(im_ndwi, cmap='seismic')
|
|
plt.colorbar()
|
|
for i,contour in enumerate(contours_wl): plt.plot(contour[:, 1], contour[:, 0], linewidth=3, color='k')
|
|
plt.axis('image')
|
|
plt.title('Detected water lines')
|
|
plt.show()
|
|
|
|
return contours_wl
|
|
|
|
def convert_pix2world(points, crs_vec):
|
|
"""
|
|
Converts pixel coordinates (row,columns) to world projected coordinates
|
|
performing an affine transformation
|
|
|
|
KV WRL 2018
|
|
|
|
Arguments:
|
|
-----------
|
|
points: np.ndarray or list of np.ndarray
|
|
array with 2 columns (rows first and columns second)
|
|
crs_vec: np.ndarray
|
|
vector of 6 elements [Xtr, Xscale, Xshear, Ytr, Yshear, Yscale]
|
|
|
|
Returns: -----------
|
|
points_converted: np.ndarray or list of np.ndarray
|
|
converted coordinates, first columns with X and second column with Y
|
|
|
|
"""
|
|
|
|
# make affine transformation matrix
|
|
aff_mat = np.array([[crs_vec[1], crs_vec[2], crs_vec[0]],
|
|
[crs_vec[4], crs_vec[5], crs_vec[3]],
|
|
[0, 0, 1]])
|
|
# create affine transformation
|
|
tform = transform.AffineTransform(aff_mat)
|
|
|
|
if type(points) is list:
|
|
points_converted = []
|
|
# iterate over the list
|
|
for i, arr in enumerate(points):
|
|
tmp = arr[:,[1,0]]
|
|
points_converted.append(tform(tmp))
|
|
|
|
elif type(points) is np.ndarray:
|
|
tmp = points[:,[1,0]]
|
|
points_converted = tform(tmp)
|
|
|
|
else:
|
|
print('invalid input type')
|
|
raise
|
|
|
|
return points_converted
|
|
|
|
def convert_epsg(points, epsg_in, epsg_out):
|
|
"""
|
|
Converts from one spatial reference to another using the epsg codes
|
|
|
|
KV WRL 2018
|
|
|
|
Arguments:
|
|
-----------
|
|
points: np.ndarray or list of np.ndarray
|
|
array with 2 columns (rows first and columns second)
|
|
epsg_in: int
|
|
epsg code of the spatial reference in which the input is
|
|
epsg_out: int
|
|
epsg code of the spatial reference in which the output will be
|
|
|
|
Returns: -----------
|
|
points_converted: np.ndarray or list of np.ndarray
|
|
converted coordinates
|
|
|
|
"""
|
|
|
|
# define input and output spatial references
|
|
inSpatialRef = osr.SpatialReference()
|
|
inSpatialRef.ImportFromEPSG(epsg_in)
|
|
outSpatialRef = osr.SpatialReference()
|
|
outSpatialRef.ImportFromEPSG(epsg_out)
|
|
# create a coordinates transform
|
|
coordTransform = osr.CoordinateTransformation(inSpatialRef, outSpatialRef)
|
|
# transform points
|
|
if type(points) is list:
|
|
points_converted = []
|
|
# iterate over the list
|
|
for i, arr in enumerate(points):
|
|
points_converted.append(np.array(coordTransform.TransformPoints(arr)))
|
|
|
|
elif type(points) is np.ndarray:
|
|
points_converted = np.array(coordTransform.TransformPoints(points))
|
|
|
|
else:
|
|
print('invalid input type')
|
|
raise
|
|
|
|
return points_converted
|
|
|
|
def classify_sand_unsupervised(im_ms_ps, im_pan, cloud_mask, wl_pix, buffer_size, min_beach_size, plot_bool):
|
|
"""
|
|
Classifies sand pixels using an unsupervised algorithm (Kmeans)
|
|
|
|
KV WRL 2018
|
|
|
|
Arguments:
|
|
-----------
|
|
im_ms_ps: np.ndarray
|
|
Pansharpened RGB + downsampled NIR and SWIR
|
|
im_pan:
|
|
Panchromatic band
|
|
cloud_mask: np.ndarray
|
|
2D cloud mask with True where cloud pixels are
|
|
wl_pix: list of np.ndarray
|
|
list of arrays containig the pixel coordinates of the water line
|
|
buffer_size: int
|
|
radius of the disk used to create a buffer around the water line
|
|
min_beach_size: int
|
|
minimum number of connected pixels belonging to a single beach
|
|
plot_bool: boolean
|
|
True if plot is wanted
|
|
|
|
Returns: -----------
|
|
im_sand: np.ndarray
|
|
2D binary image containing True where sand pixels are located
|
|
|
|
"""
|
|
# reshape the 2D images into vectors
|
|
vec_ms_ps = im_ms_ps.reshape(im_ms_ps.shape[0] * im_ms_ps.shape[1], im_ms_ps.shape[2])
|
|
vec_pan = im_pan.reshape(im_pan.shape[0]*im_pan.shape[1])
|
|
vec_mask = cloud_mask.reshape(im_ms_ps.shape[0] * im_ms_ps.shape[1])
|
|
# add B,G,R,NIR and pan bands to the vector of features
|
|
vec_features = np.zeros((vec_ms_ps.shape[0], 5))
|
|
vec_features[:,[0,1,2,3]] = vec_ms_ps[:,[0,1,2,3]]
|
|
vec_features[:,4] = vec_pan
|
|
|
|
# create binary image with ones where the detected water lines is
|
|
im_buffer = np.zeros((im_ms_ps.shape[0], im_ms_ps.shape[1]))
|
|
for i, contour in enumerate(wl_pix):
|
|
indices = [(int(_[0]), int(_[1])) for _ in list(np.round(contour))]
|
|
for j, idx in enumerate(indices):
|
|
im_buffer[idx] = 1
|
|
# perform a dilation on the binary image
|
|
se = morphology.disk(buffer_size)
|
|
im_buffer = morphology.binary_dilation(im_buffer, se)
|
|
vec_buffer = (im_buffer == 1).reshape(im_ms_ps.shape[0] * im_ms_ps.shape[1])
|
|
# add cloud mask to buffer
|
|
vec_buffer= np.logical_and(vec_buffer, ~vec_mask)
|
|
# perform kmeans (6 clusters)
|
|
kmeans = KMeans(n_clusters=6, random_state=0).fit(vec_features[vec_buffer,:])
|
|
labels = np.ones((len(vec_mask))) * np.nan
|
|
labels[vec_buffer] = kmeans.labels_
|
|
im_labels = labels.reshape(im_ms_ps.shape[0], im_ms_ps.shape[1])
|
|
# find the class with maximum reflection in the B,G,R,Pan
|
|
im_sand = im_labels == np.argmax(np.mean(kmeans.cluster_centers_[:,[0,1,2,4]], axis=1))
|
|
im_sand = morphology.remove_small_objects(im_sand, min_size=min_beach_size, connectivity=2)
|
|
# im_sand = morphology.binary_dilation(im_sand, morphology.disk(1))
|
|
|
|
if plot_bool:
|
|
im = np.copy(im_ms_ps)
|
|
im[im_sand,0] = 0
|
|
im[im_sand,1] = 0
|
|
im[im_sand,2] = 1
|
|
plt.figure()
|
|
plt.imshow(im[:,:,[2,1,0]])
|
|
plt.axis('image')
|
|
plt.title('Sand classification')
|
|
plt.show()
|
|
|
|
return im_sand
|