reconstruct_height_field_from_gradient — Reconstruct a surface from surface gradients.
reconstruct_height_field_from_gradient(Gradient : HeightField : ReconstructionMethod, GenParamName, GenParamValue : )
reconstruct_height_field_from_gradient reconstructs a surface from
the surface gradients that are given in Gradient. The surface
is returned as a height field, i.e., an image in which the gray value of each
image point corresponds to a relative height.
The reconstruction is done by integrating the gradients by different
algorithms that can be selected in the parameter
ReconstructionMethod. Because gradient fields are typically
non-integrable due to noise, the various algorithms return a solution in a
least-squares sense. The algorithms differ in the way how they model the
boundary condition. Currently three algorithms are supported:
'fft_cyclic', 'rft_cyclic' and 'poisson'.
Reconstruction with Fast Fourier transforms
The variants 'fft_cyclic' and 'rft_cyclic' assume that the image function is cyclic at the boundaries. Note that due to the assumed cyclic image function artifacts may occur at the image boundaries. Thus, in most cases, we recommend to use the 'poisson' algorithm instead.
The difference between 'fft_cyclic' and 'rft_cyclic' is that
the rft version has faster processing times and requires less memory than
the fft version. While theoretically fft and rft should return the same
result, the fft version is numerically slightly more accurate. As
reconstruct_height_field_from_gradient internally uses a fast Fourier
transform, the run time of the operator can be influenced by a previous call
to optimize_fft_speed or optimize_rft_speed, respectively.
Reconstruction according to Poisson
The 'poisson' algorithm assumes that the image has constant gradients
at the image border. In most cases, it is the recommended reconstruction
method for reconstruct_height_field_from_gradient. Its run time can
only be optimized by setting GenParamName to 'optimize_speed'
and GenParamValue to 'standard', 'patient', or
'exhaustive'. These parameters are described in more detail with the
description of optimize_fft_speed.
Note that by default, the 'poisson' algorithm uses a cache that
depends on the image size and that speeds up the reconstruction
significantly, provided that all images have the same size. The cache is
allocated at the first time when the 'poisson' algorithm is
called. Therefore the first call always takes longer than subsequent
calls. The additionally needed memory corresponds to the memory needed for
the specific size of one image. Please note that when calling the operator
with different image sizes, the cache needs to be reallocated, which leads to
a longer processing time. In this case it may be preferable to not use the
cache. To switch off the caching, you must set the parameter
GenParamName to 'caching' and the parameter
GenParamValue to 'no_cache'. The cache can explicitly be
deallocated by setting GenParamName to 'caching' and
GenParamValue to 'free_cache'. However, in the majority of
cases, we recommend to use the cache, i.e., to use the default setting for
the parameter 'caching'.
Saving and loading optimization parameters
The optimization parameters for all algorithms can be saved and loaded by
write_fft_optimization_data and read_fft_optimization_data.
Non obvious applications
Please note that the operator reconstruct_height_field_from_gradient
has various non-obvious applications, especially in the field called gradient
domain manipulation technique. In many applications, the gradient values that
are passed as input to the operator do not have the semantics of surface
gradients (i.e., the first derivatives of the height values), but are rather
the first derivatives of other kinds of parameters, typically gray values
(then, the gradients have the semantics of gray value edges). When processing
these gradient images by various means, e.g., by adding or subtracting
images, or by a filtering, the original gradient values are altered and the
subsequent call to reconstruct_height_field_from_gradient delivers a
modified image, in which, e.g., unwanted edges are removed or the contrast
has been changed locally. Typical applications are noise removal, seamless
fusion of images, or high dynamic range compression.
reconstruct_height_field_from_gradient takes into account the values of
all pixels in Gradient, not only the values within its domain.
If Gradient does not have a full domain, one could cut out the
relevant square part of the gradient field and generate a
smaller image with full domain.
Gradient (input_object) singlechannelimage → object (vector_field)
The gradient field of the image.
HeightField (output_object) image → object (real)
Reconstructed height field.
ReconstructionMethod (input_control) string → (string)
Type of the reconstruction method.
Default value: 'poisson'
List of values: 'fft_cyclic', 'poisson', 'rft_cyclic'
GenParamName (input_control) string-array → (string)
Names of the generic parameters.
Default value: []
List of values: 'caching', 'optimize_speed'
GenParamValue (input_control) integer-array → (integer / real / string)
Values of the generic parameters.
Default value: []
List of values: 'exhaustive', 'free_cache', 'no_cache', 'patient', 'standard', 'use_cache'
If the parameters are valid reconstruct_height_field_from_gradient
returns the value TRUE. If necessary, an exception is raised.
M. Kazhdan, M. Bolitho, and H. Hoppe: “Poisson Surface Reconstruction.” Symposium on Geometry Processing (June 2006).
3D Metrology