{"id":18728,"date":"2022-11-01T19:13:01","date_gmt":"2022-11-01T13:43:01","guid":{"rendered":"https:\/\/jassweb.com\/solved\/solved-extracting-the-elements-matching-the-filter\/"},"modified":"2022-11-01T19:13:01","modified_gmt":"2022-11-01T13:43:01","slug":"solved-extracting-the-elements-matching-the-filter","status":"publish","type":"post","link":"https:\/\/jassweb.com\/solved\/solved-extracting-the-elements-matching-the-filter\/","title":{"rendered":"[Solved] Extracting the elements matching the filter"},"content":{"rendered":"

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I’m basing this answer on a very similar answer I wrote just a few hours ago.<\/p>\n

#from sklearn.feature_extraction.image import extract_patches  # similar to numpy's stride_tricks\nfrom numpy.lib.stride_tricks import as_strided\n\ndata = np.array([[1, 1 , 0 , 0 , 0 , 0 , 1 , 0],\n                 [1, 1 , 1 , 0 , 0 , 1 , 1 , 0],\n                 [1, 1 , 1 , 1 , 1 , 0 , 0 , 0],\n                 [0, 0 , 1 , 1 , 1 , 0 , 0 , 0],\n                 [0, 0 , 1 , 1 , 1 , 1 , 0 , 1],\n                 [1, 1 , 0 , 0 , 0 , 1 , 1 , 1],\n                 [1, 1 , 0 , 0 , 0 , 1 , 1 , 1]])\npatches = as_strided(data, shape=(data.shape[0]-2,data.shape[1]-2, 3, 3), strides=data.strides*2)\ndual = patches.all(axis=-1).all(axis=-1)\npatches[dual==False] = 0\npatches[dual] = 1\n<\/code><\/pre>\n
The result (in data<\/code>) is as you’ve shown.<\/p>\n
The way this works is as follows:
\nthe function extract_patches<\/code> generates a view<\/em> into the array data<\/code>, which means it is not<\/em> a copy of the actual data but uses the strides<\/em> to generate a seemingly different array. In this case, it will generate all possible 3×3 submatrices (which can be overlapping) of the array data<\/code>. Then, by writing patches.all(axis=-1).all(axis=-1)<\/code>, you are first checking if the elements in the rows of the submatrices are all True (or equivalent to True in a boolean sense, so not 0, empty lists, empty dictionaries, empty tuples and a few other special cases), thereby collapsing one of the axes of this array and then with the second .all(axis=-1)<\/code> the columns are being checked to see if they’re all True.<\/p>\n
Small example of this paragraph to clarify visually:<\/p>\n
>>> A = np.array([\n... [1, 1, 0],        # -> along this row, not all elements are 1: so `all` along the last axis will return False\n... [1, 1, 1],        # -> along this row, all elements are 1: so `all` along the last axis (axis=-1) will return True\n... [1, 1, 1]])\n>>> A.all(axis=-1)\narray([False,  True,  True], dtype=bool)  # so it is done along the last axis, along the rows\n>>> A.all(axis=-1).all(axis=-1)\nFalse\n<\/code><\/pre>\n
So this array dual<\/code> now has a “1” (True actually) for every 3×3 submatrix that was full of ones. Those submatrices are overlapping however, so you first want to set the patches all to 0 whenevery any of these 3×3 submatrices was not all ones (that’s the one-to-last line in the first code block: patches[dual==False] = 0<\/code>) and then<\/em> you can apply the ones again in each 3×3 submatrix that originally had all ones.
\nThe alternatives are to correlate with a kernel = np.ones((3,3))<\/code> or to take multiple bitwise operations into account (like in the other answer), but that last method becomes very difficult to write when the array’s dimensions grow beyond simply (2,2)<\/code>.<\/p>\n<\/p><\/div>\n
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            5<\/span> <\/p><\/div>\n<\/div>\n
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solved Extracting the elements matching the filter <\/p>\n","protected":false},"excerpt":{"rendered":"
[ad_1] I’m basing this answer on a very similar answer I wrote just a few hours ago. #from sklearn.feature_extraction.image import extract_patches # similar to numpy’s stride_tricks from numpy.lib.stride_tricks import as_strided data = np.array([[1, 1 , 0 , 0 , 0 , 0 , 1 , 0], [1, 1 , 1 , 0 , 0 , … Read more<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[320],"tags":[581,2825,1699],"class_list":["post-18728","post","type-post","status-publish","format-standard","hentry","category-solved","tag-numpy","tag-scikit-image","tag-scipy"],"yoast_head":"\n[Solved] Extracting the elements matching the filter - JassWeb<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/jassweb.com\/solved\/solved-extracting-the-elements-matching-the-filter\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"[Solved] Extracting the elements matching the filter - JassWeb\" \/>\n<meta property=\"og:description\" content=\"[ad_1] I’m basing this answer on a very similar answer I wrote just a few hours ago. #from sklearn.feature_extraction.image import extract_patches # similar to numpy's stride_tricks from numpy.lib.stride_tricks import as_strided data = np.array([[1, 1 , 0 , 0 , 0 , 0 , 1 , 0], [1, 1 , 1 , 0 , 0 , ... 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