Position determination

A method of determining the three-dimensional position of an object in a reference frame, the method comprising:

• providing three or more markers at respective reference positions, at least three of the markers being patterned to encode a plurality of bits of identification information in binary form in a series of concentric light and dark regions, the center of the concentric regions providing a reference point, wherein each marker has a respective distance from a reference plane of the reference frame, the distances varying between the markers;;
• storing information including a measure of the three-dimensional positions of the markers in the reference frame and information identifying the patterned markers;
• obtaining an image of at least a sub-set of said plurality of markers from a camera associated with the object;
• processing the image to identify the positions of said markers in the image and, for each patterned marker in the sub-set, decoding said identification information and identifying the reference point;
• and
• determining a measure of the three-dimensional position of the object in the reference frame based on said processing and decoding and based on said stored information.

A method of determining the position of an object based on identification of a plurality of markers at respective reference positions, the method comprising:

• storing pre-stored or measured marker positions as initial marker positions;
• dynamically applying correction factors to said initial marker positions to produce respective corrected marker positions;
• determining the object position based on the corrected marker positions, wherein
• said dynamically applying correction factors comprises calculating correction factors so that the corrected marker positions are corrected to become mutually self-consistent values, a rate of variation of the correction factors being limited to a pre-determined level by limiting the rate of change of correction factors.

Apparatus for determination of the three-dimensional position of an object in a reference frame, the apparatus comprising:

• a camera for mounting on an object whose position is to be determined;
• a memory arranged to store measures of the three-dimensional positions of at least three markers in the reference frame and to store information identifying patterned encoded markers which markers comprise a series of concentric shapes encoding identification information as the darkness or color of the shapes, the center of the concentric shapes of each patterned marker providing a reference point for each marker;
• image processing means arranged to process an image output by the camera to identify the positions of markers in the image, to decode information encoded in the patterned markers and to determine the position of said reference points;
• and
• position determining means arranged to determine the three-dimensional position of the object in the reference frame based on the output of the image processing means and the information stored in the memory means.

Marker apparatus for positioning in the field of view of a video camera for use in determining the relative position of the camera and the marker apparatus, the apparatus comprising:

• a base;
• a first patterned marker mounted at a first predetermined relative positions on a substantially rigid base, the first patterned marker having identification information encoded thereon in binary form as a series of concentric rings of two tones, the tones being selected to enable the marker to be keyed out of the video camera image by chroma-keying, the center of the rings providing a reference point for the marker, the first marker being at a first height from the base;
• a second patterned marker mounted at a second predetermined relative positions on a substantially rigid base, the second patterned marker having identification information encoded thereon in binary form as a series of concentric rings of two tones, the tones being selected to enable the marker to be keyed out of the video camera image by chroma-keying, the center of the rings providing a reference point for the marker, the second marker being at a second height from the base;
• a third patterned marker mounted at a third predetermined relative positions on a substantially rigid base, the third patterned marker having identification information encoded thereon in binary form as a series of concentric rings of two tones, the tones being selected to enable the marker to be keyed out of the video camera image by chroma-keying, the center of the rings providing a reference point for the marker, the third marker being at a third height from the base;
• wherein
• said first height, said second height and said third height are all mutually different, whereby a three dimensional position fix relative to the base can be obtained from the markers.

A method of determining the relative three-dimensional positions of at least one camera and an object having at least three markers mounted thereon, the relative positions of the markers and the object being substantially fixed, each marker being patterned to encode identification information in binary form as the darkness or color of a series of concentric rings, the center of the rings providing a reference point, the method comprising:

• storing the relative three dimensional positions of the markers with respect to the object and information enabling the identification information to be decoded;
• receiving an image from the camera;
• identifying the positions of the markers in the camera image;
• decoding the identification information encoded on each marker;
• determining the position of the reference point for each marker;
• and
• based on the stored information, determining a measure of the relative three-dimensional positions and orientations of said at least one camera and object.