In this paper we explore the problem of fitting a 3D morphable model to single face images using only sparse geometric features (edges and landmark points). Previous approaches to this problem are based on nonlinear optimisation of an edge-derived cost that can be viewed as forming soft correspondences between model and image edges. We propose a novel approach, that explicitly computes hard correspondences. The resulting objective function is non-convex but we show that a good initialisation can be obtained efficiently using alternating linear least squares in a manner similar to the iterated closest point algorithm. We present experimental results on both synthetic and real images and show that our approach outperforms methods that use soft correspondence and other recent methods that rely solely on geometric features.
Romdhani al @cite_32 include an edge distance cost as part of a hybrid energy function. Texture and outer (silhouette) contours are used in a similar way to LM-ICP @cite_25 where correspondence between image edges and model contours is soft''. This is achieved by applying a distance transform to an edge image. This provides a smoothly varying cost surface whose value at a pixel indicates the distance (and its gradient, the direction) to the closest edge. This idea was extended by Amberg al @cite_8 who use it in a multi-view setting and smooth the edge distance cost by averaging results with different parameters. In this way, the cost surface also encodes the saliency of an edge. Keller al @cite_18 showed that such approaches lead to a cost function that is neither continuous nor differentiable. This suggests the optimisation method must be carefully chosen.
@cite_18 @cite_25 @cite_32 @cite_8
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In this paper we take a fresh look at the problem of extracting shape from contours of human faces. We focus on two key questions: how can we robustly fit a 3D face model to a given input contour; and, how much information about shape does a single contour image convey. Our system matches silhouettes and inner contours of a PCA based Morphable Model to an input contour image. We discuss different types of contours in terms of their effect on the continuity and differentiability of related error functions and justify our choices of error function (modified Euclidean Distance Transform) and optimization algorithm (Downhill Simplex). In a synthetic test setting we explore the limits of accuracy when recovering shape and pose from a single correct input contour and find that pose is much better captured by contours than is shape. In a semi-synthetic test setting - the input images are edges extracted from photorealistic renderings of the PCA model - we investigate the robustness of our method and argue that not all discrepancies between edges and contours can be solved by the fitting process alone. Abstract This paper introduces a new method of registering point sets. The registration error is directly minimized using general-purpose non-linear optimization (the Levenberg–Marquardt algorithm). The surprising conclusion of the paper is that this technique is comparable in speed to the special-purpose Iterated Closest Point algorithm, which is most commonly used for this task. Because the routine directly minimizes an energy function, it is easy to extend it to incorporate robust estimation via a Huber kernel, yielding a basin of convergence that is many times wider than existing techniques. Finally, we introduce a data structure for the minimization based on the chamfer distance transform, which yields an algorithm that is both faster and more robust than previously described methods. We present a novel algorithm aiming to estimate the 3D shape, the texture of a human face, along with the 3D pose and the light direction from a single photograph by recovering the parameters of a 3D morphable model. Generally, the algorithms tackling the problem of 3D shape estimation from image data use only the pixels intensity as input to drive the estimation process. This was previously achieved using either a simple model, such as the Lambertian reflectance model, leading to a linear fitting algorithm. Alternatively, this problem was addressed using a more precise model and minimizing a non-convex cost function with many local minima. One way to reduce the local minima problem is to use a stochastic optimization algorithm. However, the convergence properties (such as the radius of convergence) of such algorithms, are limited. Here, as well as the pixel intensity, we use various image features such as the edges or the location of the specular highlights. The 3D shape, texture and imaging parameters are then estimated by maximizing the posterior of the parameters given these image features. The overall cost function obtained is smoother and, hence, a stochastic optimization algorithm is not needed to avoid the local minima problem. This leads to the multi-features fitting algorithm that has a wider radius of convergence and a higher level of precision. This is shown on some example photographs, and on a recognition experiment performed on the CMU-PIE image database. We present a novel model based stereo system, which accurately extracts the 3D shape and pose of faces from multiple images taken simultaneously. Extracting the 3D shape from images is important in areas such as pose-invariant face recognition and image manipulation. The method is based on a 3D morphable face model learned from a database of facial scans. The use of a strong face prior allows us to extract high precision surfaces from stereo data of faces, where traditional correlation based stereo methods fail because of the mostly textureless input images. The method uses two or more uncalibrated images of arbitrary baseline, estimating calibration and shape simultaneously. Results using two and three input images are presented. We replace the lighting and albedo estimation of a monocular method with the use of stereo information, making the system more accurate and robust. We evaluate the method using ground truth data and the standard PIE image dataset. A comparison with the state of the art monocular system shows that the new method has a significantly higher accuracy.