Beyond Straight Lines - Object Detection Using Curvature

Visual object detection in cluttered scenes is one of the key problems of computer vision. Localizing all instances of an object category is highly challenging due to the large intra-class variability. Finding a common model for all the widely diverse class instances thus poses a major difficulty.


To yield robust, powerful object representations, the vision community has now broadly adopted the theme of gradient histograms. In effect, this results in a straight line approximation of object boundaries since local regions are described by a histogram over a discrete set of edge orientations that they contain.

The examples below show that one can not distinguish a smooth curve from one with corners or from a set of differently oriented lines in an arbitrary configuration based only on histograms of oriented gradients.

Stop sign with sharp bends

Stop sign with smooth curve

Differently oriented lines in arbitrary configuration

Our approach extends the widely used object representation based on gradient orientation histograms by incorporating a robust description of curvature. Histograms of curvature are able to capture the shape information of complex objects and yields orthogonal information to the state-of-the-art theme of histograms of oriented gradients for visual search tasks.


Feature Extraction

Given an image we first compute an edge image and extract all connected line segments. After that we compute for each line segment the approximated curvature using a chord-to-point distance accumulation. This results in a curvature value for each edge pixel. The darker the colour in the example curvature images on the right the stronger the curvature.
Next the curvature information is captured in a similar way to histograms of gradients. We divide the image into connected cells and for each cell we build a 1D histogram of curvature information.

mugs bottles


We are using a Support Vector Machine (SVM) to learn a general model of the object from training data. After the training phase the performance of the classifier is tested on an independent test set. To detect an object instance on a test image the classifier is run in sliding window mode over different location and scale.


We reported our results on two challenging datasets: the ETHZ Shape Dataset and INRIA horses. The ETHZ Shape Dataset contains 255 images belonging to five different classes (Apples, Bottles, Giraffes, Mugs and Swans). The INRIA horses dataset consists of 170 images containing one or more side-viewed horses and 170 images without horses.

Our results show that the use of curvature information yields orthogonal information to the state-of-the-art theme of histograms of oriented gradients for visual search tasks. Combining both leads to better accuracy and performance on standard datasets and significantly improves state-of-the-art detection system solely based on HoG. The proposed curvature-based object representation is generic, efficient to compute, and it can be effortlessly integrated into all current object models that utilize histograms of gradients.

Images in the first column on the right show detection results using standard histogram of oriented gradient (HoG). In the second column on can see results using our method with integrated curvature histograms. Ground-truth is shown in green, first detection is shown in red and false positives with dashed lines. These examples illustrate a general finding in this database that compared to the widely used HoG, our proposed representation yields a better localization of the maxima compared to ground-truth and generation of less false-positives.


See publication section.