63,159 research outputs found
Image segmentation with adaptive region growing based on a polynomial surface model
A new method for segmenting intensity images into smooth surface segments is presented. The main idea is to divide the image into flat, planar, convex, concave, and saddle patches that coincide as well as possible with meaningful object features in the image. Therefore, we propose an adaptive region growing algorithm based on low-degree polynomial fitting. The algorithm uses a new adaptive thresholding technique with the Lâ fitting cost as a segmentation criterion. The polynomial degree and the fitting error are automatically adapted during the region growing process. The main contribution is that the algorithm detects outliers and edges, distinguishes between strong and smooth intensity transitions and finds surface segments that are bent in a certain way. As a result, the surface segments corresponding to meaningful object features and the contours separating the surface segments coincide with real-image object edges. Moreover, the curvature-based surface shape information facilitates many tasks in image analysis, such as object recognition performed on the polynomial representation. The polynomial representation provides good image approximation while preserving all the necessary details of the objects in the reconstructed images. The method outperforms existing techniques when segmenting images of objects with diffuse reflecting surfaces
Sampling and Reconstruction of Shapes with Algebraic Boundaries
We present a sampling theory for a class of binary images with finite rate of
innovation (FRI). Every image in our model is the restriction of
\mathds{1}_{\{p\leq0\}} to the image plane, where \mathds{1} denotes the
indicator function and is some real bivariate polynomial. This particularly
means that the boundaries in the image form a subset of an algebraic curve with
the implicit polynomial . We show that the image parameters --i.e., the
polynomial coefficients-- satisfy a set of linear annihilation equations with
the coefficients being the image moments. The inherent sensitivity of the
moments to noise makes the reconstruction process numerically unstable and
narrows the choice of the sampling kernels to polynomial reproducing kernels.
As a remedy to these problems, we replace conventional moments with more stable
\emph{generalized moments} that are adjusted to the given sampling kernel. The
benefits are threefold: (1) it relaxes the requirements on the sampling
kernels, (2) produces annihilation equations that are robust at numerical
precision, and (3) extends the results to images with unbounded boundaries. We
further reduce the sensitivity of the reconstruction process to noise by taking
into account the sign of the polynomial at certain points, and sequentially
enforcing measurement consistency. We consider various numerical experiments to
demonstrate the performance of our algorithm in reconstructing binary images,
including low to moderate noise levels and a range of realistic sampling
kernels.Comment: 12 pages, 14 figure
Variational Uncalibrated Photometric Stereo under General Lighting
Photometric stereo (PS) techniques nowadays remain constrained to an ideal
laboratory setup where modeling and calibration of lighting is amenable. To
eliminate such restrictions, we propose an efficient principled variational
approach to uncalibrated PS under general illumination. To this end, the
Lambertian reflectance model is approximated through a spherical harmonic
expansion, which preserves the spatial invariance of the lighting. The joint
recovery of shape, reflectance and illumination is then formulated as a single
variational problem. There the shape estimation is carried out directly in
terms of the underlying perspective depth map, thus implicitly ensuring
integrability and bypassing the need for a subsequent normal integration. To
tackle the resulting nonconvex problem numerically, we undertake a two-phase
procedure to initialize a balloon-like perspective depth map, followed by a
"lagged" block coordinate descent scheme. The experiments validate efficiency
and robustness of this approach. Across a variety of evaluations, we are able
to reduce the mean angular error consistently by a factor of 2-3 compared to
the state-of-the-art.Comment: Haefner and Ye contributed equall
A bayesian approach to simultaneously recover camera pose and non-rigid shape from monocular images
© . This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/In this paper we bring the tools of the Simultaneous Localization and Map Building (SLAM) problem from a rigid to a deformable domain and use them to simultaneously recover the 3D shape of non-rigid surfaces and the sequence of poses of a moving camera. Under the assumption that the surface shape may be represented as a weighted sum of deformation modes, we show that the problem of estimating the modal weights along with the camera poses, can be probabilistically formulated as a maximum a posteriori estimate and solved using an iterative least squares optimization. In addition, the probabilistic formulation we propose is very general and allows introducing different constraints without requiring any extra complexity. As a proof of concept, we show that local inextensibility constraints that prevent the surface from stretching can be easily integrated.
An extensive evaluation on synthetic and real data, demonstrates that our method has several advantages over current non-rigid shape from motion approaches. In particular, we show that our solution is robust to large amounts of noise and outliers and that it does not need to track points over the whole sequence nor to use an initialization close from the ground truth.Peer ReviewedPostprint (author's final draft
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