Recent advances in convolutional neural networks (CNN) have achieved remarkable results in locating objects in images. In these networks, the training procedure usually requires providing bounding boxes or the maximum number of expected objects. In this paper, we address the task of estimating object locations without annotated bounding boxes which are typically hand-drawn and time consuming to label. We propose a loss function that can be used in any fully convolutional network (FCN) to estimate object locations. This loss function is a modification of the average Hausdorff distance between two unordered sets of points. The proposed method has no notion of bounding boxes, region proposals, or sliding windows. We evaluate our method with three datasets designed to locate people's heads, pupil centers and plant centers. We outperform state-of-the-art generic object detectors and methods fine-tuned for pupil tracking.
The Hausdorff distance can be used to measure the distance between two sets of points @cite_9 . Modifications of the Hausdorff distance @cite_45 have been used for various multiple tasks, including character recognition @cite_26 , face recognition @cite_59 and scene matching @cite_59 . Schutze al @cite_56 use the average Hausdorff distance to evaluate solutions in multi-objective optimization problems. @cite_41 , Elkhiyari al compare features extracted by a CNN according to multiple variants of the Hausdorff distance for the task of face recognition. @cite_60 , Fan al use the Chamfer and Earth Mover's distance, along with a new neural network architecture, for 3D object reconstruction by estimating the location of a fixed number of points. The Hausdorff distance is also a common metric to evaluate the quality of segmentation boundaries in the medical imaging community @cite_27 @cite_28 @cite_57 @cite_61 .
@cite_61 @cite_26 @cite_60 @cite_41 @cite_28 @cite_9 @cite_56 @cite_57 @cite_27 @cite_45 @cite_59
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Abstract Hausdorff distance is an efficient measure of the similarity of two point sets. In this paper, we propose a new spatially weighted Hausdorff distance measure for human face recognition. The weighting function used in the Hausdorff distance measure is based on an eigenface, which has a large value at locations of importance facial features and can reflect the face structure more effectively. Two modified Hausdorff distances, namely, “spatially eigen-weighted Hausdorff distance” (SEWHD) and “spatially eigen-weighted ‘doubly’ Hausdorff distance” (SEW2HD) are proposed, which incorporate the information about the location of important facial features such as eyes, mouth, and face contour so that distances at those regions will be emphasized. Experimental results based on a combination of the ORL, MIT, and Yale face databases show that SEW2HD can achieve recognition rates of 83 , 90 and 92 for the first one, the first three and the first five likely matched faces, respectively, while the corresponding recognition rates of SEWHD are 80 , 83 and 88 , respectively. The Hausdorff distance measures the extent to which each point of a model set lies near some point of an image set and vice versa. Thus, this distance can be used to determine the degree of resemblance between two objects that are superimposed on one another. Efficient algorithms for computing the Hausdorff distance between all possible relative positions of a binary image and a model are presented. The focus is primarily on the case in which the model is only allowed to translate with respect to the image. The techniques are extended to rigid motion. The Hausdorff distance computation differs from many other shape comparison methods in that no correspondence between the model and the image is derived. The method is quite tolerant of small position errors such as those that occur with edge detectors and other feature extraction methods. It is shown that the method extends naturally to the problem of comparing a portion of a model against an image. > The Hausdorff distance dH is a widely used tool to measure the distance between different objects in several research fields. Possible reasons for this might be that it is a natural extension of the well-known and intuitive distance between points and or the fact that dH defines in certain cases a metric in the mathematical sense. In evolutionary multiobjective optimization (EMO) the task is typically to compute the entire solution set-the so-called Pareto set-respectively its image, the Pareto front. Hence, dH should, at least at first sight, be a natural choice to measure the performance of the outcome set in particular since it is related to the terms spread and convergence as used in EMO literature. However, so far, dH does not find the general approval in the EMO community. The main reason for this is that dH penalizes single outliers of the candidate set which does not comply with the use of stochastic search algorithms such as evolutionary strategies. In this paper, we define a new performance indicator, Δp, which can be viewed as an “averaged Hausdorff distance” between the outcome set and the Pareto front and which is composed of (slight modifications of) the well-known indicators generational distance (GD) and inverted generational distance (IGD). We will discuss theoretical properties of Δp (as well as for GD and IGD) such as the metric properties and the compliance with state-of-theart multiobjective evolutionary algorithms (MOEAs), and will further on demonstrate by empirical results the potential of Δp as a new performance indicator for the evaluation of MOEAs. The purpose of object matching is to decide the similarity between two objects. This paper introduces 24 possible distance measures based on the Hausdorff distance between two point sets. These measures can be used to match two sets of edge points extracted from any two objects. Based on experiments on synthetic images containing various levels of noise, the authors determined that one of these distance measures, called the modified Hausdorff distance (MHD) has the best performance for object matching. The advantages of MHD ever other distances are also demonstrated on several edge snaps of objects extracted from real images.