radiometric_self_calibration — Perform a radiometric self-calibration of a camera.
radiometric_self_calibration(Images : : ExposureRatios, Features, FunctionType, Smoothness, PolynomialDegree : InverseResponse)
radiometric_self_calibration performs a radiometric self-calibration of a camera. For this, at least two images that show the same image contents (scene) must be passed in Images. All images passed in Images must be acquired with different exposures. Typically, the different exposures are obtained by changing the shutter times at the camera. It is not recommended to change the exposure by changing the aperture of the lens since in this case the exposures cannot be determined accurately enough. The ratio of the exposures of consecutive images is passed in ExposureRatios. For example, a value of 0.5 specifies that the second image of an image pair has been acquired with half the exposure of the first image of the pair. The exposure ratio can easily be determined from the shutter times since the exposure is proportional to the shutter time. The exposure ratio must be greater than 0 and smaller than 1. This means that the images must be sorted according to descending exposure. ExposureRatios must contain one element less than the number of images passed in Images. If all exposure ratios are identical, as a simplification a single value can be passed in ExposureRatios.
As described above, the images passed in Images must show identical image contents. Hence, it is typically necessary that neither the camera nor the objects in the scene move. If the camera has rotated around the optical center, the images should be aligned to a reference image (one of the images) using proj_match_points_ransac and projective_trans_image. If the features used for the radiometric calibration are determined from the 2D gray value histogram of consecutive image pairs (Features = '2d_histogram'), it is essential that the images are aligned and that the objects in the scene do not move. For Features = '1d_histograms', the features used for the radiometric calibration are determined from the 1D gray value histograms of the image pairs. In this mode, the calibration can theoretically be performed if the 1D histograms of the images do not change by the movement of the objects in the images. This can, for example, be the case if an object moves in front of a uniformly textured background. However, it is preferable to use Features = '2d_histogram' because this mode is more accurate. The mode Features = '1d_histograms' should only be used if it is impossible to construct the camera set-up such that neither the camera nor the objects in the scene move.
Furthermore, care should be taken to cover the range of gray values without gaps by choosing appropriate image contents. Whether there are gaps in the range of gray values can easily be checked based on the 1D gray value histograms of the images or the 2D gray value histograms of consecutive images. In the 1D gray value histograms (see gray_histo_abs), there should be no areas between the minimum and maximum gray value that have a frequency of 0 or a very small frequency. In the 2D gray value histograms (see histo_2dim), a single connected region having the shape of a “strip” should result from a threshold operation with a lower threshold of 1. If more than one connected component results, a more suitable image content should be chosen. If the image content can be chosen such that the gray value range of the image (e.g., 0-255 for byte images) can be covered with two images with different exposures, and if there are no gaps in the histograms, the two images suffice for the calibration. This, however, is typically not the case, and hence multiple images must be used to cover the entire gray value range. As described above, for this multiple images with different exposures must be taken to cover the entire gray value range as well as possible. For this, normally the first image should be exposed such that the maximum gray value is slightly below the saturation limit of the camera, or such that the image is significantly overexposed. If the first image is overexposed, a significant overexposure is necessary to enable radiometric_self_calibration to detect the overexposed areas reliably. If the camera exhibits an unusual saturation behavior (e.g., a saturation limit that lies significantly below the maximum gray value) the overexposed areas should be masked out by hand with reduce_domain in the overexposed image.
radiometric_self_calibration returns the inverse gray value response function of the camera in InverseResponse. The inverse response function can be used to create an image with a linear response by using InverseResponse as the LUT in lut_trans. The parameter FunctionType determines which function model is used to model the response function. For FunctionType = 'discrete', the response function is described by a discrete function with the relevant number of gray values (256 for byte images). For FunctionType = 'polynomial', the response is described by a polynomial of degree PolynomialDegree. The computation of the response function is slower for FunctionType = 'discrete'. However, since a polynomial tends to oscillate in the areas in which no gray value information can be derived, even if smoothness constraints are imposed as described below, the discrete model should usually be preferred over the polynomial model.
The inverse response function is returned as a tuple of integer values for FunctionType = 'discrete' and FunctionType = 'polynomial'. In some applications, it might be desirable to return the inverse response function as floating point values to avoid the numerical error that is introduced by rounding. For example, if the inverse response function must be inverted to obtain the response function of the camera, there is some loss of information if the values are returned as integers. For these applications, FunctionType can be set to 'discrete_real' or 'polynomial_real', in which case the inverse response function will be returned as a tuple of floating point numbers.
The parameter Smoothness defines (in addition to the constraints on the response function that can be derived from the images) constraints on the smoothness of the response function. If, as described above, the gray value range can be covered completely and without gaps, the default value of 1 should not be changed. Otherwise, values > 1 can be used to obtain a stronger smoothing of the response function, while values < 1 lead to a weaker smoothing. The smoothing is particularly important in areas for which no gray value information can be derived from the images, i.e., in gaps in the histograms and for gray values smaller than the minimum gray value of all images or larger than the maximum gray value of all images. In these areas, the smoothness constraints lead to an interpolation or extrapolation of the response function. Because of the nature of the internally derived constraints, FunctionType = 'discrete' favors an exponential function in the undefined areas, whereas FunctionType = 'polynomial' favors a straight line. Please note that the interpolation and extrapolation is always less reliable than to cover the gray value range completely and without gaps. Therefore, in any case it should be attempted first to acquire the images optimally, before the smoothness constraints are used to fill in the remaining gaps. In all cases, the response function should be checked for plausibility after the call to radiometric_self_calibration. In particular, it should be checked whether InverseResponse is monotonic. If this is not the case, a more suitable scene should be used to avoid interpolation, or Smoothness should be set to a larger value. For FunctionType = 'polynomial', it may also be necessary to change PolynomialDegree. If, despite these changes, an implausible response is returned, the saturation behavior of the camera should be checked, e.g., based on the 2D gray value histogram, and the saturated areas should be masked out by hand, as described above.
When the inverse gray value response function of the camera is determined, the absolute energy falling on the camera cannot be determined. This means that InverseResponse can only be determined up to a scale factor. Therefore, an additional constraint is used to fix the unknown scale factor: the maximum gray value that can occur should occur for the maximum input gray value, e.g., InverseResponse = 255 for byte images. This constraint usually leads to the most intuitive results. If, however, a multichannel image (typically an RGB image) should be radiometrically calibrated (for this, each channel must be calibrated separately), the above constraint may lead to the result that a different scaling factor is determined for each channel. This may lead to the result that gray tones no longer appear gray after the correction. In this case, a manual white balancing step must be carried out by identifying a homogeneous gray area in the original image, and by deriving appropriate scaling factors from the corrected gray values for two of the three response curves (or, in general, for n-1 of the n channels). Here, the response curve that remains invariant should be chosen such that all scaling factors are < 1. With the scaling factors thus determined, new response functions should be calculated by multiplying each value of a response function with the scaling factor corresponding to that response function.
Ratio of the exposure energies of successive image pairs.
Default value: 0.5
Suggested values: 0.25, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8
Restriction: ExposureRatios > 0 && ExposureRatios < 1
Features that are used to compute the inverse response function of the camera.
Default value: '2d_histogram'
List of values: '1d_histograms', '2d_histogram'
Type of the inverse response function of the camera.
Default value: 'discrete'
List of values: 'discrete', 'discrete_real', 'polynomial', 'polynomial_real'
Smoothness of the inverse response function of the camera.
Default value: 1.0
Suggested values: 0.3, 0.5, 0.7, 0.8, 1.0, 1.2, 1.5, 2.0, 3.0
Restriction: Smoothness > 0
Degree of the polynomial if FunctionType = 'polynomial'.
Default value: 5
Suggested values: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10
Restriction: PolynomialDegree >= 1 && PolynomialDegree <= 20
Inverse response function of the camera.
open_framegrabber ('1394IIDC', 1, 1, 0, 0, 0, 0, 'default', -1, \ 'default', -1, 'default', 'default', 'default', \ -1, -1, AcqHandle) * Define appropriate shutter times. Shutters := [1000,750,500,250,125] Num := |Shutters| * Grab and accumulate images with the different exposures. In this * loop, it must be ensured that the scene remains static. gen_empty_obj (Images) for I := 0 to Num-1 by 1 set_framegrabber_param (AcqHandle, 'shutter', Shutters[I]) grab_image (Image, AcqHandle) concat_obj (Images, Image, Images) endfor * Compute the exposure ratios from the shutter times. ExposureRatios := real(Shutters[1:Num-1])/real(Shutters[0:Num-2]) radiometric_self_calibration (Images, ExposureRatios, '2d_histogram', \ 'discrete', 1, 5, InverseResponse) * Note that if the frame grabber supports hardware LUTs, we could * also call set_framegrabber_lut here instead of lut_trans below. * This would be more efficient. while (1) grab_image_async (Image, AcqHandle, -1) lut_trans (Image, ImageLinear, InverseResponse) * Process radiometrically correct image. * [...] endwhile close_framegrabber (AcqHandle)
If the parameters are valid, the operator radiometric_self_calibration returns the value 2 (H_MSG_TRUE). If necessary an exception is raised.
read_image, grab_image, grab_image_async, set_framegrabber_param, concat_obj, proj_match_points_ransac, proj_match_points_ransac_guided, projective_trans_image
histo_2dim, gray_histo, gray_histo_abs, reduce_domain