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Otherwise, must be one of 2 or 3." } ] } ] } ] } ], "title": [], "level": 0, "target": null }, "Extended Summary": { "__type": "Section", "__tag": 4015, "children": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Has the following form in 2D " } ] }, { "__type": "Code", "__tag": 4050, "value": "X = a0 * x - b0 * y + a1 =\n = s * x * cos(rotation) - s * y * sin(rotation) + a1\n\nY = b0 * x + a0 * y + b1 =\n = s * x * sin(rotation) + s * y * cos(rotation) + b1", "execution_status": null }, { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "where " }, { "__type": "InlineCode", "__tag": 4051, "value": "s" }, { "__type": "Text", "__tag": 4046, "value": " is a scale factor and the homogeneous transformation matrix is " } ] }, { "__type": "Code", "__tag": 4050, "value": "[[a0 -b0 a1]\n [b0 a0 b1]\n [0 0 1 ]]", "execution_status": null }, { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "The similarity transformation extends the Euclidean transformation with a single scaling factor in addition to the rotation and translation parameters." } ] }, { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "The implicit parameters are applied in the following order:" } ] }, { "__type": "BulletList", "__tag": 4053, "ordered": true, "start": 1, "children": [ { "__type": "ListItem", "__tag": 4054, "children": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Scale;" } ] } ] }, { "__type": "ListItem", "__tag": 4054, "children": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Rotation;" } ] } ] }, { "__type": "ListItem", "__tag": 4054, "children": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Translation." } ] } ] } ] } ], "title": [], "level": 0, "target": null }, "Other Parameters": { "__type": "Section", "__tag": 4015, "children": [], "title": [], "level": 0, "target": null } }, "_ordered_sections": [ "Summary", "Extended Summary", "Parameters", "Returns", "Yields", "Receives", "Raises", "Warns", "Other Parameters", "Attributes", "Methods", "Notes", "Warnings" ], "item_file": "/dev/scikit-image/src/skimage/transform/_geometric.py", "item_line": 2073, "item_type": "ABCMeta", "aliases": [ "skimage.transform.SimilarityTransform" ], "example_section_data": { "__type": "Section", "__tag": 4015, "children": [ { "__type": "Code", "__tag": 4050, "value": "import numpy as np\nimport skimage as ski\n", "execution_status": "success" }, { "__type": "Text", "__tag": 4046, "value": "\nDefine a transform with an homogeneous transformation matrix:\n\n" }, { "__type": "Code", "__tag": 4050, "value": "tform = ski.transform.SimilarityTransform(np.diag([2., 3., 1.]))\ntform.params\n", "execution_status": "success" }, { "__type": "Text", "__tag": 4046, "value": "\nDefine a transform with parameters:\n\n" }, { "__type": "Code", "__tag": 4050, "value": "tform = ski.transform.SimilarityTransform(\n rotation=0.2, translation=[1, 2])\nnp.round(tform.params, 2)\n", "execution_status": "success" }, { "__type": "Text", "__tag": 4046, "value": "\nYou can estimate a transformation to map between source and destination\npoints:\n\n" }, { "__type": "Code", "__tag": 4050, "value": "src = np.array([[150, 150],\n [250, 100],\n [150, 200]])\ndst = np.array([[200, 200],\n [300, 150],\n [150, 400]])\ntform = ski.transform.SimilarityTransform.from_estimate(src, dst)\nnp.allclose(tform.params, [[ 1.79, 0.21, -142.86],\n [-0.21, 1.79, 21.43],\n [ 0. , 0. , 1. ]], atol=0.01)\n", "execution_status": "success" }, { "__type": "Text", "__tag": 4046, "value": "\nApply the transformation to some image data.\n\n" }, { "__type": "Code", "__tag": 4050, "value": "img = ski.data.astronaut()\nwarped = ski.transform.warp(img, inverse_map=tform.inverse)\n", "execution_status": "success" }, { "__type": "Text", "__tag": 4046, "value": "\nThe estimation can fail - for example, if all the input or output points\nare the same. If this happens, you will get a transform that is not\n\"truthy\" - meaning that ``bool(tform)`` is ``False``:\n\n" }, { "__type": "Code", "__tag": 4050, "value": "if tform:\n print(\"Estimation succeeded.\")\nbad_src = np.ones((3, 2))\nbad_tform = ski.transform.SimilarityTransform.from_estimate(\n bad_src, dst)\nif not bad_tform:\n print(\"Estimation failed.\")\n", "execution_status": "success" }, { "__type": "Text", "__tag": 4046, "value": "\nTrying to use this failed estimation transform result will give a suitable\nerror:\n\n" }, { "__type": "Code", "__tag": 4050, "value": "bad_tform.params # doctest: +IGNORE_EXCEPTION_DETAIL\n", "execution_status": "success" } ], "title": [], "level": 0, "target": null }, "see_also": [], "signature": { "__type": "SignatureNode", "__tag": 4029, "kind": "function", "parameters": [ { "__type": "SigParam", "__tag": 4030, "name": "matrix", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "POSITIONAL_OR_KEYWORD", "default": "None" }, { "__type": "SigParam", "__tag": 4030, "name": "scale", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "KEYWORD_ONLY", "default": "None" }, { "__type": "SigParam", "__tag": 4030, "name": "rotation", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "KEYWORD_ONLY", "default": "None" }, { "__type": "SigParam", "__tag": 4030, "name": "translation", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "KEYWORD_ONLY", "default": "None" }, { "__type": "SigParam", "__tag": 4030, "name": "dimensionality", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "KEYWORD_ONLY", "default": "None" } ], "return_annotation": { "__type": "Empty", "__tag": 4031 }, "target_name": "SimilarityTransform" }, "references": null, "qa": "skimage.transform._geometric:SimilarityTransform", "arbitrary": [], "local_refs": [ "dimensionality", "matrix", "params", "rotation", "scale", "translation" ] }