We propose three algorithms as approximations to k-means++ with complexity only O(nk) which is independent of D with n being the number of data points, k being the number of clusters and D the dimensionality. By combining random projection and k-means++, the proposed algorithm still enjoying the lower-bounded performance by results given for k-means++, on the other hand, the errors introduced by the approximation are also bounded by JL lemma, which is sufficently low in the experiment we presented. By approximating D(x)2in the k-means++ algorithm, we obtain an approximate algorithm to k-means++ of complexity only O(nk). The approximation to D(x)2can be obtained through random projections by only perturbing the distances to a provably small extent. Our experiments on real-world datasets show that, when k is small, the performance of minimization of the potential deteriorated only by 3%-5% while the execution time can be shortened to 50% of the original. With a large k, compared to the results of our proposed algorithms with small values of k, the error introduced by random projection is much reduced and the speed up of the execution time is improved. In our experiments, it is shown that the speed up of the proposed algorithms is up to 20 times compared to k-means++.

We boost the efficiency and robustness of distribution-based matching by random subsampling which results in the minimum number of samples required to achieve a specified probability that a candidate sampling distribution is a good approximation to the model distribution. The improvement is demonstrated with applications to object detection, mean-shift tracking using color distributions and tracking with improved robustness for low-resolution video sequences. The problem of minimizing the number of samples required for robust distribution matching is formulated as a constrained optimization problem with the specified probability as the objective function. We show that surprisingly mean-shift tracking using our method requires very few samples. Our experiments demonstrate that robust tracking can be achieved with even as few as 5 random samples from the distribution of the target candidate. This leads to a considerably reduced computational complexity that is also independent of object size. We show that random subsampling speeds up tracking by two orders of magnitude for typical object sizes.

Existing approaches to learning-based face image super-resolution require low-resolution testing inputs manually registered to pre-aligned highresolution training models [9, 12, 13, 5]. This restricts automatic applications to live images and video. In this paper, we propose a multi-resolution patch tensor based model to automatically super-resolve and register low-resolution testing face images. Face candidates are triggered first by a face detector giving the subwindows with their coarse initial positions and scales in a large image frame. This initialises a combined registration and super-resolution process. Rather than manually aligning each coarsely detected face subwindow to some predefined template, based on its position and scale, we scan all the potential face subwindows across different positions and scales, and obtain registration and super-resolution in a simultaneous process. The superresolution result which is optimally correlated to its original low-resolution face subwindow is also guaranteed to be the best super-resolved reconstruction. We verify our approach by experimenting on MIT+CMU face detection dataset, the promising results demonstrate the robustness of our approach on learning-based face super-resolution on real images. 1

In this work, boosting the efficiency of Mean-Shift Tracking using random sampling is proposed. We obtained the surprising result that mean-shift tracking requires only very few samples. Our experiments demonstrate that robust tracking can be achieved with as few as even 5 random samples from the image of the object. As the computational complexity is considerably reduced and becomes independent of object size, the processor can be used to handle other processing tasks while tracking. It is demonstrated that random sampling significantly reduces the processing time by two orders of magnitude for typical object sizes. Additionally, with random sampling, we propose a new optimal on-line feature selection algorithm for object tracking which maximizes a similarity measure for the weights of the RGB channels. It selects the weights of the RGB channels which discriminate the object and the background the most using Steepest Descent. Moreover, the spatial distribution of pixels representing the object is estimated for spatial weighting. Arbitrary spatial weighting is incorporated into Mean-Shift Tracking to represent objects with arbitrary or changing shapes by picking up non-uniform random samples. Experimental results demonstrate that our tracker with online feature selection and arbitrary spatial weighting outperforms the original mean-shift tracker with improved computational efficiency and tracking accuracy. 1

In this work, we present a framework for tracking objects in changing views by finding the subwindow most likely to be the object using Haar-like features selected by AdaBoost as the representation. Probabilistic AdaBoost [14] is used to derive the objective function. In addition, the projective warping of 2D features is used to track 3D objects in non-frontal views in real time. Transformed 2D features can approximate relatively flat object structures such as the two eyes in a face. In this paper, it is shown that, under weak perspective projection, the projective warping of a rectangle feature can be approximated by a similarity transform with an additional free parameter. Since features in non-frontal views are computed on-the-fly by projective transforms under weak perspective projection, our framework requires only frontal-view training samples to track objects in multiple views. 1