Shape-from-Template (SfT) solves 3D vision from a single image and a deformable 3D object model, called a template. Concretely, SfT computes registration (the correspondence between the template and the image) and reconstruction (the depth in camera frame). It constrains the object deformation to quasi-isometry. Real-time and automatic SfT represents an open problem for complex objects and imaging conditions. We present four contributions to address core unmet challenges to realise SfT with a Deep Neural Network (DNN). First, we propose a novel DNN called DeepSfT, which encodes the template in its weights and hence copes with highly complex templates. Second, we propose a semi-supervised training procedure to exploit real data. This is a practical solution to overcome the render gap that occurs when training only with simulated data. Third, we propose a geometry adaptation module to deal with different cameras at training and inference. Fourth, we combine statistical learning with physics-based reasoning. DeepSfT runs automatically and in real-time and we show with numerous experiments and an ablation study that it consistently achieves a lower 3D error than previous work. It outperforms in generalisation and achieves great performance in terms of reconstruction and registration error with wide-baseline, occlusions, illumination changes, weak texture and blur.

Non-Rigid Structure-from-Motion (NRSfM) reconstructs a deformable 3D object from keypoint correspondences established between monocular 2D images. Current NRSfM methods lack statistical robustness, which is the ability to cope with correspondence errors. This prevents one to use automatically established correspondences, which are prone to errors, thereby strongly limiting the scope of NRSfM. We propose a three-step automatic pipeline to solve NRSfM robustly by exploiting isometry. Step (i) computes the optical flow from correspondences, step (ii) reconstructs each 3D point's normal vector using multiple reference images and integrates them to form surfaces with the best reference and step (iii) rejects the 3D points that break isometry in their local neighborhood. Importantly, each step is designed to discard or flag erroneous correspondences. Our contributions include the robustification of optical flow by warp estimation, new fast analytic solutions to local normal reconstruction and their robustification, and a new scale-independent measure of 3D local isometric coherence. Experimental results show that our robust NRSfM method consistently outperforms existing methods on both synthetic and real datasets.

A major research area in Computer Assisted Intervention (CAI) is to aid laparoscopic surgery teams with Augmented Reality (AR) guidance. This involves registering data from other modalities such as MR and fusing it with the laparoscopic video in real-time, to reveal the location of hidden critical structures. We present the first system for AR guided laparoscopic surgery of the uterus. This works with pre-operative MR or CT data and monocular laparoscopes, without requiring any additional interventional hardware such as optical trackers. We present novel and robust solutions to two main sub-problems: the initial registration, which is solved using a short exploratory video, and update registration, which is solved with real-time tracking-by-detection. These problems are challenging for the uterus because it is a weakly-textured, highly mobile organ that moves independently of surrounding structures. In the broader context, our system is the first that has successfully performed markerless real-time registration and AR of a mobile human organ with monocular laparoscopes in the OR.

3D reconstruction of deformable objects using inter-image visual motion from monocular images has been studied under Shape-from-Template (SfT) and Non-Rigid Structure-from-Motion (NRSfM). Most methods have been developed for simple deformation models, primarily isometry. They may treat a surface as a discrete set of points and draw constraints from the points only or they may use a non-parametric representation and use both points and differentials to express constraints. We propose a differential framework based on Cartan's theory of connections and moving frames. It is applicable to SfT and NRSfM, and to deformation models other than isometry. It utilises infinitesimal-level assumptions on the surface's geometry and mappings. It has the following properties. 1) It allows one to derive existing solutions in a simpler way. 2) It models SfT and NRSfM in a unified way. 3) It allows us to introduce a new skewless deformation model and solve SfT and NRSfM for it. 4) It facilitates a generic solution to SfT which does not require deformation modeling. Our framework is complete: it solves deformable 3D reconstruction for a whole class of algebraic deformation models including isometry. We compared our solutions with the state-of-the-art methods and show that ours outperform in terms of both accuracy and computation time.

This work proposes a new method for face and mouth tracking using video cameras. This method has been proposed to be used in intelligent spaces as an initial stage to provide information to higher level applications. The method incorporates the classifiers of the Viola and Jones detection method, modified to provide a probabilistic output previously proposed by the authors, useful for tracking with particle filter. The method combines classifiers trained to detect specific poses (frontal and side face views), building an independent likelihood model of pose changes. We also propose to combine the model in several cameras to allow the mouth tracking in a three-dimensional space. The system has been evaluated on the AV16.3 database sequences showing good results in both precision and recall when using a single camera (in a bidimensional space), and an error below 3cm when using three cameras (in a three-dimensional space).

An indoor positioning fusion sensor composed of a five infrared detector set and one camera is presented in this work. The position of the target is obtained by hyperbolic trilateration from phase-difference measurements with the infrared sensor and by an homography with the camera. Subsequent fusion is carried out with a maximum likelihood estimator. A model is proposed for the infrared and camera observation variances and their propagation to the fusion estimation covariance matrix. The system shows cm-level accuracy in infrared multipath-free conditions and good matching with the model. Real measurements are conducted to assess sensor performance, also compared with Monte Carlo simulations for model validation. The evaluation of the fusion sensor performance is specially focused on its dependence on the camera resolution, tested at three resolution levels.

We present a global and convex formulation for the template-less 3D reconstruction of a deforming object with the perspective camera. We show for the first time how to construct a Second-Order Cone Programming (SOCP) problem for Non-Rigid Structure-from-Motion (NRSfM) using the Maximum-Depth Heuristic (MDH). In this regard, we deviate strongly from the general trend of using affine cameras and factorization-based methods to solve NRSfM, which do not perform well with complex nonlinear deformations. In MDH, the points' depths are maximized so that the distance between neighbouring points in camera space are upper bounded by the geodesic distance. In NRSfM both geodesic and camera space distances are unknown. We show that, nonetheless, given point correspondences and the camera's intrinsics the whole problem can be solved with SOCP. This is the first convex formulation for NRSfM with physical constraints. We further present how robustness and temporal continuity can be included in the formulation to handle outliers and decrease the problem size, respectively. We show with extensive experiments that our methods accurately reconstruct quasi-isometric objects from partial views under articulated and strong deformations. Compared to the previous methods, our approach gives better or similar accuracy. It naturally handles missing correspondences, non-smooth objects and is very simple to implement compared to previous methods, with only one free parameter (the neighbourhood size).

We study Isometric Non-Rigid Shape-from-Motion (Iso-NRSfM): given multiple intrinsically calibrated monocular images, we want to reconstruct the time-varying 3D shape of a thin-shell object undergoing isometric deformations. We show that Iso-NRSfM is solvable from local warps, the inter-image geometric transformations. We propose a new theoretical framework based on the Riemmanian manifold to represent the unknown 3D surfaces as embeddings of the camera's retinal plane. This allows us to use the manifold's metric tensor and Christoffel Symbol (CS) fields. These are expressed in terms of the first and second order derivatives of the inverse-depth of the 3D surfaces, which are the unknowns for Iso-NRSfM. We prove that the metric tensor and the CS are related across images by simple rules depending only on the warps. This forms a set of important theoretical results. We show that current solvers cannot solve for the first and second order derivatives of the inverse-depth simultaneously. We thus propose an iterative solution in two steps. 1) We solve for the first order derivatives assuming that the second order derivatives are known. We initialise the second order derivatives to zero, which is an infinitesimal planarity assumption. We derive a system of two cubics in two variables for each image pair. The sum-of-squares of these polynomials is independent of the number of images and can be solved globally, forming a well-posed problem for $N\geq 3$ images. 2) We solve for the second order derivatives by initialising the first order derivatives from the previous step. We solve a linear system of $4N-4$ equations in three variables. We iterate until the first order derivatives converge. The solution for the first order derivatives gives the surfaces' normal fields which we integrate to recover the 3D surfaces. The proposed method outperforms existing work in terms of accuracy and computation cost on synthetic and real datasets.

Shape-from-Template (SfT) reconstructs the shape of a deforming surface from a single image, a 3D template and a deformation prior. For isometric deformations, this is a well-posed problem. However, previous methods which require no initialization break down when the perspective effects are small, which happens when the object is small or viewed from larger distances. That is, they do not handle all projection geometries. We propose stable SfT methods that accurately reconstruct the 3D shape for all projection geometries. We follow the existing approach of using first-order differential constraints and obtain local analytical solutions for depth and the first-order quantities: the depth-gradient or the surface normal. Previous methods use the depth solution directly to obtain the 3D shape. We prove that the depth solution is unstable when the projection geometry tends to affine, while the solution for the first-order quantities remain stable for all projection geometries. We therefore propose to solve SfT by first estimating the first-order quantities (either depth-gradient or surface normal) and integrating them to obtain shape. We validate our approach with extensive synthetic and real-world experiments and obtain significantly more accurate results compared to previous initialization-free methods. Our approach does not require any optimization, which makes it very fast.

We present a global and convex formulation for template-less 3D reconstruction of a deforming object with the perspective camera. We show for the first time how to construct a Second-Order Cone Programming (SOCP) problem for Non-Rigid Shape-from-Motion (NRSfM) using the Maximum-Depth Heuristic (MDH). In this regard, we deviate strongly from the general trend of using affine cameras and factorization-based methods to solve NRSfM. In MDH, the points' depths are maximized so that the distance between neighbouring points in camera space are upper bounded by the geodesic distance. In NRSfM both geodesic and camera space distances are unknown. We show that, nonetheless, given point correspondences and the camera's intrinsics the whole problem is convex and solvable with SOCP. We show with extensive experiments that our method accurately reconstructs quasi-isometric surfaces from partial views under articulated and strong deformations. It naturally handles missing correspondences, non-smooth objects and is very simple to implement compared to previous methods, with only one free parameter (the neighbourhood size).

We study Isometric Non-Rigid Shape-from-Motion (Iso-NRSfM): given multiple intrinsically calibrated monocular images, we want to reconstruct the time-varying 3D shape of an object undergoing isometric deformations. We show that Iso-NRSfM is solvable from the warps (the inter-image geometric transformations). We propose a new theoretical framework based on Riemmanian manifolds to represent the unknown 3D surfaces, as embeddings of the camera's retinal planes. This allows us to use the manifolds' metric tensor and Christoffel Symbol fields, which we prove are related across images by simple rules depending only on the warps. This forms a set of important theoretical results. Using the infinitesimal planarity formulation, it then allows us to derive a system of two quartics in two variables for each image pair. The sum-of-squares of these polynomials is independent of the number of images and can be solved globally, forming a well-posed problem for N ≥ 3 images, whose solution directly leads to the surface's normal field. The proposed method outperforms existing work in terms of accuracy and computation cost on synthetic and real datasets.

We have developed a technique to study how good computers can be at diagnosing gastrointestinal lesions from regular (white light and narrow banded) colonoscopic videos compared to two levels of clinical knowledge (expert and beginner). Our technique includes a novel tissue classification approach which may save clinician's time by avoiding chromoendoscopy, a time-consuming staining procedure using indigo carmine. Our technique also discriminates the severity of individual lesions in patients with many polyps, so that the gastroenterologist can directly focus on those requiring polypectomy. Technically, we have designed and developed a framework combining machine learning and computer vision algorithms, which performs a virtual biopsy of hyperplastic lesions, serrated adenomas and adenomas. Serrated adenomas are very difficult to classify due to their mixed/hybrid nature and recent studies indicate that they can lead to colorectal cancer through the alternate serrated pathway. Our approach is the first step to avoid systematic biopsy for suspected hyperplastic tissues. We also propose a database of colonoscopic videos showing gastrointestinal lesions with ground truth collected from both expert image inspection and histology. We not only compare our system with the expert predictions, but we also study if the use of 3D shape features improves classification accuracy, and compare our technique's performance with three competitor methods.

Shape-from-Template (SfT) is the problem of inferring the shape of a deformable object as observed in an image using a shape template. We call 2DSfT the `usual' instance of SfT where the shape is a surface embedded in 3D and the image a 2D projection. We introduce 1DSfT, a novel instance of SfT where the shape is a curve embedded in 2D and the image a 1D projection. We focus on isometric deformations, for which 2DSfT is a well-posed problem, and admits an analytical local solution which may be used to initialize nonconvex refinement. Through a complete theoretical study of 1DSfT with perspective projection, we show that it is related to 2DSfT, but may have very different properties: (i) 1DSfT cannot be exactly solved locally and (ii) 1DSfT cannot be solved uniquely, as it has a discrete amount of at least two solutions. We then propose two convex initialization algorithms, a local analytical one based on infinitesimal planarity and a global one based on inextensibility. We show how nonconvex refinement can be implemented where, contrarily to current 2DSfT methods, one may enforce isometry exactly using a novel angle-based parameterization. Finally, our method is tested with simulated and real data.

We propose a novel formulation of the generalized cross correlation with phase transform (GCC-PHAT) for a pair of microphones in diffuse sound field. This formulation elucidates the links between the microphone distances and the GCC-PHAT output. Hence, it leads to a new model that enables estimation of the pairwise distances by optimizing over the distances best matching the GCC-PHAT observations. Furthermore, the relation of this model to the coherence function is elaborated along with the dependency on the signal bandwidth. The experiments conducted on real data recordings demonstrate the theories and support the effectiveness of the proposed method.

The objective of Shape-from-Template (SfT) is to infer an object's shape from a single image and a 3D object template. Existing methods are called thin-shell SfT as they represent the object by its outer surface. This may be an open surface for thin objects such as a piece of paper or a closed surface for thicker objects such as a ball. We propose volumetric SfT, which specifically handles objects of the latter kind. Volumetric SfT uses the object's full volume to express the deformation constraints and reconstructs the object's surface and interior deformation. This is a challenging problem because for opaque objects, only a part of the outer surface is visible in the image. Inspired by mesh-editing techniques, we use an As-Rigid-As-Possible (ARAP) deformation model that softly imposes local rigidity. We formalise ARAP isometric SfT as a constrained variational optimisation problem which we solve using iterative optimisation. We present strategies to find an initial solution based on thin-shell SfT and volume propagation. Experiments with synthetic and real data show that our method has a typical maximum relative error of 5% in reconstructing the deformation of an entire object, including its back and interior for which no visual data is available.

We study a problem that we call Shape-from-Template, which is the problem of reconstructing the shape of a deformable surface from a single image and a 3D template. Current methods in the literature address the case of isometric deformations, and relax the isometry constraint to the convex inextensibility constraint, solved using the so-called maximum depth heuristic. We call these methods zeroth-order since they use image point locations (the zeroth-order differential structure) to solve the shape inference problem from a perspective image. We propose a novel class of methods that we call first-order. The key idea is to use both image point locations and their first-order differential structure. The latter can be easily extracted from a warp between the template and the input image. We give a unified problem formulation as a system of PDEs for isometric and conformal surfaces that we solve analytically. This has important consequences. First, it gives the first analytical algorithms to solve this type of reconstruction problems. Second, it gives the first algorithms to solve for the exact constraints. Third, it allows us to study the well-posedness of this type of reconstruction: we establish that isometric surfaces can be reconstructed unambiguously and that conformal surfaces can be reconstructed up to a few discrete ambiguities and a global scale. In the latter case, the candidate solution surfaces are obtained analytically. Experimental results on simulated and real data show that our isometric methods generally perform as well as or outperform state of the art approaches in terms of reconstruction accuracy, while our conformal methods largely outperform all isometric methods for extensible deformations.

Employment interviews are relevant scenarios for the study of social interaction. In this setting, social skills play an important role, even though the interactions between potential employers and candidates are often limited. One fundamental aspect of social interaction is the use of nonverbal communication , which affects how we are socially perceived. We present a method to automatically extract body communicative cues from one-on-one conversations recorded with Kinect devices. First, we find the three-dimensional position of hands and head of the subject, and, aided by training data, we infer the upper body pose. Then, we use the inferred poses to perform action recognition and build person-specific activity descriptors. We evaluate our system with both domain-specific and public, generic datasets, and show competitive performance.

It has been recently shown that reconstructing an isometric surface from a single 2D input image matched to a 3D template was a well-posed problem. This however does not tell us how reconstruction algorithms will behave in practical conditions, where the amount of perspective is generally small and the projection thus behaves like weak-perspective or orthography. We here bring answers to what is theoretically recoverable in such imaging conditions, and explain why existing convex numerical solutions and analytical solutions to 3D reconstruction may be unstable. We then propose a new algorithm which works under all imaging conditions, from strong to loose perspective. We empirically show that the gain in stability is tremendous, bringing our results close to the iterative minimization of a statistically-optimal cost. Our algorithm has a low complexity, is simple and uses only one round of linear least-squares.

We address the problem of body communication retrieval and measuring in seated conversations by means of markerless motion capture. In psychological studies, the use of automatic methods is key to reduce the subjectivity present in manual behavioral coding used to extract these cues. These studies usually involve hundreds of subjects with different clothing, non-acted poses, or different distances to the camera in uncalibrated, RGB-only video. However, range cameras are not yet common in psychology research, especially in existing recordings. Therefore, it becomes highly relevant to develop a fast method that is able to work in these conditions. Given the known relationship between depth and motion estimates, we propose to robustly integrate highly appearance-invariant image motion features in a machine learning approach, complemented with an effective tracking scheme. We evaluate the method's performance with existing databases and a database of upper body poses displayed in job interviews that we make public, showing that in our scenario it is comparable to that of Kinect without using a range camera, and state-of-the-art w.r.t. the HumanEva and ChaLearn 2011 evaluation datasets.

We present a robust method to automatically detect blinks in video sequences of conversations, aimed to discovering stress. Psychological studies have shown a relationship between blink frequency and dopamine levels, which in turn are affected by stress. Task performance correlates through an inverted U shape to both dopamine and stress levels. This shows the importance of automatic blink detection as a way of reducing human coding burden. We use an off-the-shelf face tracker in order to extract the eye region. Then, we perform per-pixel classification of the extracted eye images to later identify blinks through their dynamics. We evaluate the performance of our system with a job interview database with annotations of psychological variables, and show statistically significant correlation between perceived stress resistance and the automatically detected blink patterns.

An active research objective in Computer Assisted Intervention (CAI) is to develop guidance systems to aid surgical teams in laparoscopic Minimal Invasive Surgery (MIS) using Augmented Reality (AR). This involves registering and fusing additional data from other modalities and overlaying it onto the laparoscopic video in realtime. We present the first AR-based image guidance system for assisted myoma localisation in uterine laparosurgery. This involves a framework for semi-automatically registering a pre-operative Magnetic Resonance Image (MRI) to the laparoscopic video with a deformable model. Although there has been several previous works involving other organs, this is the first to tackle the uterus. Furthermore, whereas previous works perform registration between one or two laparoscopic images (which come from a stereo laparoscope) we show how to solve the problem using many images (e.g. 20 or more), and show that this can dramatically improve registration. Also unlike previous works, we show how to integrate occluding contours as registration cues. These cues provide powerful registration constraints and should be used wherever possible. We present retrospective qualitative results on a patient with two myomas and quantitative semi-synthetic results. Our multi-image framework is quite general and could be adapted to improve registration in other organs with other modalities such as CT.

This paper studies the problem of surface reconstruction from a single image, given a template of the surface. We investigate the variational structure of the reconstruction problem for isometric and conformal deformations and weak-perspective camera projections. We give analytical solutions for the surface shape given that the registration warp between the template and the input image meets specific differential constraints. We explore those constraints, giving an optimization strategy to compute warps that comply with isometric and conformal deformations under weak-perspective projection. We study the performance of the proposed algorithms with synthetic and real datasets. The experiments show that surface reconstruction with weak-perspective is accurate when using cameras with large focal lengths and improves state of the art methods.

We study the uncalibrated isometric Shape-from-Template problem, that consists in estimating an isometric deformation from a template shape to an input image whose focal length is unknown. Our method is the first that combines the following features: solving for both the 3D deformation and the camera's focal length, involving only local analytical solutions (there is no numerical optimization), being robust to mismatches, handling general surfaces and running extremely fast. This was achieved through two key steps. First, an `uncalibrated' 3D deformation is computed thanks to a novel piecewise weak-perspective projection model. Second, the camera's focal length is estimated and enables upgrading the 3D deformation to metric. We use a variational framework, implemented using a smooth function basis and sampled local deformation models. The only degeneracy -which we easily detect- for focal length estimation is a flat and fronto-parallel surface. Experimental results on simulated and real datasets show that our method achieves a 3D shape accuracy slightly below state of the art methods using a precalibrated or the true focal length, and a focal length accuracy slightly below static calibration methods.

The Viola and Jones face detectors and Particle Filters are great algorithms for face detections and target tracking. However Viola outputs a binary result, while Particle Filters work with probabilistic inputs. This is the reason why there are not so many works that combine both algorithms. A probabilistic model or likelihood functions to transform Viola and Jones output to probabilistic data are needed to allow linking both methods. In this work we explore some Viola and Jones based likelihood functions presented in literature, and propose new strategies. We also extend the evaluation of the likelihood functions in position, scale and pose. One of our proposed functions shows better characteristics to be used in intelligent spaces in three dimensional face tracking applications.

This paper presents an algorithm that automatically corrects the distortion caused by multipath interference (MpI) in depth measurements obtained with time of flight cameras (ToF cameras). A radiometric model that explains, under some mild simplifications, the working principle of a ToF camera including a model for MpI is proposed. Using this model we demonstrate that all the information needed for compensating the influence of MpI on the scene captured by the camera is self-contained in the measurements (depth and amplitude of infrared signal). We propose an iterative optimization method that, based on the measurements contaminated with MpI, gives depth correction for each pixel. Results are shown in artificially generated time of flight scenes using the radiometric model. In addition, the system has been validated in real scenes using a commercial ToF camera providing good results.

This paper deals with generalized procrustes analysis. This is the problem of registering a set of shape data by estimating a reference shape and a set of rigid transformations given point correspondences. The transformed shape data must align with the reference shape as best possible. This is a difficult problem. The classical approach computes alternatively the reference shape, usually as the average of the transformed shapes, and each transformation in turn. We propose a global approach to generalized procrustes analysis for two- and three-dimensional shapes. It uses modern convex optimization based on the theory of Sum Of Squares functions. We show how to convert the whole procrustes problem, including missing data, into a semidefinite program. Our approach is statistically grounded: it finds the maximum likelihood estimate. We provide results on synthetic and real datasets. Compared to classical alternation our algorithm obtains lower errors. The discrepancy is very high when similarities are estimated or when the shape data have significant deformations.

In many different problems, data analysis requires one to first compensate for a global transformation between the different datasets of shape data. This is known as procrustes analysis in the statistics and shape analysis literature [1, 3]. More precisely, it is called generalized procrustes analysis when more than two shape data are to be registered. In this problem, one global transformation per observed shape has to be computed, so that the shapes are mapped to a common coordinate frame whereby they look as ‘similar ’ as possible. This process is called also rigid registration. The classical approach to generalized procrustes analysis is to select one of the shapes as a reference shape, and register each of the other shapes to the reference in turn by solving the absolute orientation problem. It is common to then alternate a re-estimation of the reference shape, as the average of the registered shapes, with shape registration. We call this general paradigm the alternation approach to generalized procrustes analysis. Both iterative [2] and algebraic closed-form solutions [4] were

This article presents a control solution for the guidance of wheeled convoy units in non-linear trajectories. The proposal consists of a Mamdani fuzzy controller to solve the Decentralized Control problem as applied to a set of units following a leader, whilst guaranteeing the so called "string stability " condition of the convoy. Fuzzy control design is described for each of the follower units, whose action is determined by their own motion state, that of its predecessor and the leader's trajectory. The "string stability" is ensured by the adjustment of the linear velocity transfer function for each unit. Results are given for simulated and experimental trials carried out with P3-DX robot units sharing a wireless network.

This paper deals with shading and AAMs. Shading is created by lighting change. It can be of two types: self- shading and external shading. The effect of self-shading can be explicitly learned and handled by AAMs. This is not however possible for external shading, which is usually dealt with by robustifying the cost function. We take a different approach: we measure the fitting cost in a so-called Light-Invariant space. This approach naturally handles self-shading and external shading. The framework is based on mild assumptions on the scene reflectance and the cameras. Some photometric camera response parameters are required. We propose to estimate these while fitting an existing color AAM in a photometric 'self-calibration' manner. We report successful results with a face AAM with test images taken indoor under simple lighting change.

In this paper a ring of calibrated and synchronized cameras is used for achieving robot and obstacle localization inside a common observed area. To avoid complex appearance matching derived from the wide-baseline arrangement of cameras, a metric occupancy grid is obtained by intersection of silhouettes projected onto the floor. A particle filter is proposed for tracking multiple objects by using the grid as observation data. A clustering algorithm is included in the filter to increase the robustness and adaptability of the multimodal estimation task. To preserve identity of the robot from the set of tracked objects, odometry readings are used to compute a maximum likelihood (ML) global trajectory identification. As a proof of concept, real results are obtained in a long sequence with a mobile robot moving in a human-cluttered scene.

The work described in this paper explores a new solution for tracking multiple and dynamic objects in complex environments. An XPF (extended particle filter) is used to implement a multimodal distribution that represents the most probable estimation for each object position and velocity. A standard PF (particle filter) cannot be used with a variable number of obstacles; some other solutions have been tested in different previous works, but most of them require heavy computational resources at least for a high number of obstacles to be tracked. The solution described here includes a clustering procedure that increases the robustness of the probabilistic process in order to provide on-line adaptation to the variable number of clusters. The result is the XPFCP: extended particle filter with clustering process. The presented algorithm has been tested using stereovision measurements; the results included in the paper show the efficiency of the proposed system.