Finding pixel position in an image based on coordinates

[samlama111]

I am able to search for an image of a polygon, but I would like to specifically locate it. Is there a way of achieving this, based on its coordinates?

I have tried the georeferencing mentioned in the documentation, but without success. I try calculate the (xa, ya) position, but as a result I get a ya position of 27998.858461163214, well outside of the bounds of the image (its height is 8578 pixels). Only difference to documenation is our assumption that Z=Zc. We expect ~(5750, 3350), but receive (5147, 27998).

Following is the geojson and georeferencing calculation. Any help is greatly appreciated!

1. I query data using the /search/ endpoint, with the following example response:

   "geometry": {
               "type": "Polygon",
               "coordinates": [
                   [
                       [
                           711020.0,
                           6166399.999999999
                       ],
                       [
                           710825.0,
                           6167520.0
                       ],
                       [
                           712076.0,
                           6167500.0
                       ],
                       [
                           711888.0,
                           6166390.000000001
                       ],
                       [
                           711020.0,
                           6166399.999999999
                       ]
                   ]
               ]
           },
           "bbox": [
               710825.0,
               6166390.000000001,
               712076.0,
               6167520.0
           ],
           "properties": {
               "datetime": "2019-05-05T08:55:38Z",
               "gsd": 0.1,
               "license": "various",
               "platform": "Fixed-wing aircraft",
               "instruments": [
                   "PhaseOne-IXU-RS-1000_RS011009"
               ],
               "providers": [
                   {
                       "name": "MGGP_Aero",
                       "roles": [
                           "producer"
                       ]
                   },
                   {
                       "url": "https://sdfi.dk/",
                       "name": "SDFI",
                       "roles": [
                           "licensor",
                           "host"
                       ]
                   }
               ],
               "proj:epsg": null,
               "proj:shape": [
                   8578.0,
                   11478.0
               ],
               "direction": "north",
               "estimated_accuracy": 0.01,
               "pers:omega": 44.7639,
               "pers:phi": 0.709278,
               "pers:kappa": -0.560045,
               "pers:perspective_center": [
                   711481.37,
                   6165370.14,
                   1492.23
               ],
               "pers:crs": 25832,
               "pers:vertical_crs": 5799,
               "pers:rotation_matrix": [
                   0.9998756105860587,
                   0.00177663759250761,
                   -0.015671851008138338,
                   0.009773724690373558,
                   0.7100659311567243,
                   0.7040673602122247,
                   0.012378920018853833,
                   -0.7041329540430549,
                   0.7099602421049842
               ],
               "pers:interior_orientation": {
                   "camera_id": "PhaseOne-IXU-RS-1000_RS011009",
                   "focal_length": 108.2201,
                   "pixel_spacing": [
                       0.0046,
                       0.0046
                   ],
                   "calibration_date": "2019-02-21",
                   "principal_point_offset": [
                       0.0,
                       0.0
                   ],
                   "sensor_array_dimensions": [
                       11478.0,
                       8578.0
                   ]
               },
               "asset:data": "https://cdn.dataforsyningen.dk/skraafoto_server/COG_oblique_2019/10km_616_71/1km_6166_711/2019_85_47_2_0044_00001106.tif",
               "asset:thumbnail": "..."
           },

2. Pixel calculation:

   
   props = item["properties"]
   m11, m12, m13, m21, m22, m23, m31, m32, m33 = props["pers:rotation_matrix"]
   Xc, Yc, Zc = props["pers:perspective_center"]
   f_mm = props["pers:interior_orientation"]["focal_length"]
   ppo_x, ppo_y = props["pers:interior_orientation"]["principal_point_offset"]
   pixel_size = props["pers:interior_orientation"]["pixel_spacing"][0]
   sensor_cols, sensor_rows = props["pers:interior_orientation"]["sensor_array_dimensions"]

Calculated values. In pixels. Origo in image lower left.

f = f_mm / pixel_size x0 = sensor_cols 0.5 + ppo_x / pixel_size y0 = sensor_rows 0.5 + ppo_y / pixel_size

X = (item['bbox'][0] + item['bbox'][2]) / 2 Y = (item['bbox'][1] + item['bbox'][3]) / 2 Z = Zc # We assume the Z coordinate of the polygon is the same

dX = (X-Xc) dY = (Y-Yc) dZ = (Z-Zc)

n = (m31 dX + m32 dY + m33 * dZ)

xa = x0 - f (m11 dX + m12 dY + m13 dZ) / n ya = y0 - f (m21 dX + m22 dY + m23 dZ) / n

[NicolaiLolansen]

The assumption of Z = Zc is where it goes wrong. You actually want the Z coordinate for the corresponding pixel on the ground. There are various ways to find this, but a quick way to see that the other calculations you made are correct, is to assign Z a value closer to the ground, could be between 10-30.

For the real value of Z you need a terrain model. See https://datafordeler.dk/dataoversigt/danmarks-hoejdemodel-dhm/dhm-wms/