{
  "__type": "IngestedDoc",
  "__tag": 4010,
  "_content": {
    "Notes": {
      "__type": "Section",
      "__tag": 4015,
      "children": [],
      "title": [],
      "level": 0,
      "target": null
    },
    "Warns": {
      "__type": "Section",
      "__tag": 4015,
      "children": [],
      "title": [],
      "level": 0,
      "target": null
    },
    "Raises": {
      "__type": "Section",
      "__tag": 4015,
      "children": [],
      "title": [],
      "level": 0,
      "target": null
    },
    "Yields": {
      "__type": "Section",
      "__tag": 4015,
      "children": [],
      "title": [],
      "level": 0,
      "target": null
    },
    "Methods": {
      "__type": "Section",
      "__tag": 4015,
      "children": [],
      "title": [],
      "level": 0,
      "target": null
    },
    "Returns": {
      "__type": "Section",
      "__tag": 4015,
      "children": [],
      "title": [],
      "level": 0,
      "target": null
    },
    "Summary": {
      "__type": "Section",
      "__tag": 4015,
      "children": [
        {
          "__type": "Paragraph",
          "__tag": 4045,
          "children": [
            {
              "__type": "Text",
              "__tag": 4046,
              "value": "2D polynomial transformation."
            }
          ]
        }
      ],
      "title": [],
      "level": 0,
      "target": null
    },
    "Receives": {
      "__type": "Section",
      "__tag": 4015,
      "children": [],
      "title": [],
      "level": 0,
      "target": null
    },
    "Warnings": {
      "__type": "Section",
      "__tag": 4015,
      "children": [],
      "title": [],
      "level": 0,
      "target": null
    },
    "Attributes": {
      "__type": "Section",
      "__tag": 4015,
      "children": [
        {
          "__type": "Parameters",
          "__tag": 4026,
          "children": [
            {
              "__type": "DocParam",
              "__tag": 4016,
              "name": "params",
              "annotation": "ndarray of shape (2, N)",
              "desc": [
                {
                  "__type": "Paragraph",
                  "__tag": 4045,
                  "children": [
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": "Polynomial coefficients where "
                    },
                    {
                      "__type": "InlineRole",
                      "__tag": 4003,
                      "value": "N * 2 = (order + 1) * (order + 2)",
                      "domain": null,
                      "role": null,
                      "inventory": null
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": ". So, a_ji is defined in "
                    },
                    {
                      "__type": "InlineRole",
                      "__tag": 4003,
                      "value": "params[0, :]",
                      "domain": null,
                      "role": null,
                      "inventory": null
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": " and b_ji in "
                    },
                    {
                      "__type": "InlineRole",
                      "__tag": 4003,
                      "value": "params[1, :]",
                      "domain": null,
                      "role": null,
                      "inventory": null
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": "."
                    }
                  ]
                }
              ]
            }
          ]
        }
      ],
      "title": [],
      "level": 0,
      "target": null
    },
    "Parameters": {
      "__type": "Section",
      "__tag": 4015,
      "children": [
        {
          "__type": "Parameters",
          "__tag": 4026,
          "children": [
            {
              "__type": "DocParam",
              "__tag": 4016,
              "name": "params",
              "annotation": "array_like of shape (2, N), optional",
              "desc": [
                {
                  "__type": "Paragraph",
                  "__tag": 4045,
                  "children": [
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": "Polynomial coefficients where "
                    },
                    {
                      "__type": "InlineRole",
                      "__tag": 4003,
                      "value": "N * 2 = (order + 1) * (order + 2)",
                      "domain": null,
                      "role": null,
                      "inventory": null
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": ". So, a_ji is defined in "
                    },
                    {
                      "__type": "InlineRole",
                      "__tag": 4003,
                      "value": "params[0, :]",
                      "domain": null,
                      "role": null,
                      "inventory": null
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": " and b_ji in "
                    },
                    {
                      "__type": "InlineRole",
                      "__tag": 4003,
                      "value": "params[1, :]",
                      "domain": null,
                      "role": null,
                      "inventory": null
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": "."
                    }
                  ]
                }
              ]
            },
            {
              "__type": "DocParam",
              "__tag": 4016,
              "name": "dimensionality",
              "annotation": "int, optional",
              "desc": [
                {
                  "__type": "Paragraph",
                  "__tag": 4045,
                  "children": [
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": "Must have value 2 (the default) for polynomial transforms."
                    }
                  ]
                }
              ]
            }
          ]
        }
      ],
      "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      "
            }
          ]
        },
        {
          "__type": "Code",
          "__tag": 4050,
          "value": "X = sum[j=0:order]( sum[i=0:j]( a_ji * x**(j - i) * y**i ))\nY = sum[j=0:order]( sum[i=0:j]( b_ji * x**(j - i) * y**i ))",
          "execution_status": null
        }
      ],
      "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": 2259,
  "item_type": "ABCMeta",
  "aliases": [
    "skimage.transform.PolynomialTransform"
  ],
  "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 transformation by estimation:\n\n"
      },
      {
        "__type": "Code",
        "__tag": 4050,
        "value": "src = [[-12.3705, -10.5075],\n       [-10.7865, 15.4305],\n       [8.6985, 10.8675],\n       [11.4975, -9.5715],\n       [7.8435, 7.4835],\n       [-5.3325, 6.5025],\n       [6.7905, -6.3765],\n       [-6.1695, -0.8235]]\ndst = [[0, 0],\n       [0, 5800],\n       [4900, 5800],\n       [4900, 0],\n       [4479, 4580],\n       [1176, 3660],\n       [3754, 790],\n       [1024, 1931]]\ntform = ski.transform.PolynomialTransform.from_estimate(src, dst)\n",
        "execution_status": "success"
      },
      {
        "__type": "Text",
        "__tag": 4046,
        "value": "\nCalling the transform applies the transformation to the points:\n\n"
      },
      {
        "__type": "Code",
        "__tag": 4050,
        "value": "pts = tform(src)\nnp.allclose(pts, [[   7.54,   12.27],\n                  [   2.98, 5796.95],\n                  [4870.44, 5766.59],\n                  [4889.72,   -6.72],\n                  [4515.62, 4617.5 ],\n                  [1183.25, 3694.  ],\n                  [3767.57,  800.53],\n                  [ 998.02, 1881.97]], atol=0.01)\n",
        "execution_status": "success"
      }
    ],
    "title": [],
    "level": 0,
    "target": null
  },
  "see_also": [],
  "signature": {
    "__type": "SignatureNode",
    "__tag": 4029,
    "kind": "function",
    "parameters": [
      {
        "__type": "SigParam",
        "__tag": 4030,
        "name": "params",
        "annotation": {
          "__type": "Empty",
          "__tag": 4031
        },
        "kind": "POSITIONAL_OR_KEYWORD",
        "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": "PolynomialTransform"
  },
  "references": null,
  "qa": "skimage.transform._geometric:PolynomialTransform",
  "arbitrary": [],
  "local_refs": [
    "dimensionality",
    "params"
  ]
}