We formulate a general energy and method for segmentation that is designed to have preference for segmenting the coarse structure over the fine structure of the data, without smoothing across boundaries of regions. The energy is formulated by considering data terms at a continuum of scales from the scale space computed from the Heat Equation within regions, and integrating these terms over all time. We show that the energy may be approximately optimized without solving for the entire scale space, but rather solving time-independent linear equations at the native scale of the image, making the method computationally feasible. We provide a multi-region scheme, and apply our method to motion segmentation. Experiments on a benchmark dataset shows that our method is less sensitive to clutter or other undesirable fine-scale structure, and leads to better performance in motion segmentation.
Since we apply our method to the problem of segmenting moving objects in video based on motion, we highlight some aspects of that literature most relevant to this work. Methods for motion segmentation are based on optical flow (e.g., @cite_0 ). Piecewise parametric models for motion of regions in segmentation are used in e.g., @cite_40 @cite_18 . Non-parametric warps are used for motion models (e.g., @cite_7 @cite_17 @cite_12 ). Our goal here is to estimate motion, but rather we use existing techniques for motion estimation, and improve the segmentation of regions by replacing the data term with our novel energy.
@cite_18 @cite_7 @cite_0 @cite_40 @cite_12 @cite_17
1548690188 2082869876 2143033699 2171116555
We propose to tackle the optical flow problem by a combination of two recent advances in the computation of dense correspondences, namely the incorporation of image segmentation and robust global optimization via graph-cuts. In the first step, each segment (extracted by colour segmentation) is assigned to an affine motion model from a set of sparse correspondences. Using a layered model, we then identify those motion models that represent the dominant image motion. This layer extraction task is accomplished by optimizing a simple energy function that operates in the domain of segments via graph-cuts. We then estimate the spatial extent that is covered by each layer and identify occlusions. Since treatment of occlusions is hardly possible when using entire segments as matching primitives, we propose to use the pixel level in addition. We therefore define an energy function that measures the quality of an assignment of segments and pixels to layers. This energy function is then extended to work on multiple input frames and minimized via graph-cuts. In the experimental results, we show that our method produces good-quality results, especially in regions of low texture and close to motion boundaries, which are challenging tasks in optical flow computation. We present an unsupervised approach for learning a layered representation of a scene from a video for motion segmentation. Our method is applicable to any video containing piecewise parametric motion. The learnt model is a composition of layers, which consist of one or more segments. The shape of each segment is represented using a binary matte and its appearance is given by the rgb value for each point belonging to the matte. Included in the model are the effects of image projection, lighting, and motion blur. Furthermore, spatial continuity is explicitly modeled resulting in contiguous segments. Unlike previous approaches, our method does not use reference frame(s) for initialization. The two main contributions of our method are: (i) A novel algorithm for obtaining the initial estimate of the model by dividing the scene into rigidly moving components using efficient loopy belief propagation; and (ii) Refining the initial estimate using ? β-swap and ?-expansion algorithms, which guarantee a strong local minima. Results are presented on several classes of objects with different types of camera motion, e.g. videos of a human walking shot with static or translating cameras. We compare our method with the state of the art and demonstrate significant improvements. We suggest a variational method for the joint estimation of optic flow and the segmentation of the image into regions of similar motion. It makes use of the level set framework following the idea of motion competition, which is extended to non-parametric motion. Moreover, we automatically determine an appropriate initialization and the number of regions by means of recursive two-phase splits with higher order region models. The method is further extended to the spatiotemporal setting and the use of additional cues like the gray value or color for the segmentation. It need not fear a quantitative comparison to pure optic flow estimation techniques: For the popular Yosemite sequence with clouds we obtain the currently most accurate result. We further uncover a mistake in the ground truth. Coarsely correcting this, we get an average angular error below 1 degree. In moving camera videos, motion segmentation is commonly performed using the image plane motion of pixels, or optical flow. However, objects that are at different depths from the camera can exhibit different optical flows even if they share the same real-world motion. This can cause a depth-dependent segmentation of the scene. Our goal is to develop a segmentation algorithm that clusters pixels that have similar real-world motion irrespective of their depth in the scene. Our solution uses optical flow orientations instead of the complete vectors and exploits the well-known property that under camera translation, optical flow orientations are independent of object depth. We introduce a probabilistic model that automatically estimates the number of observed independent motions and results in a labeling that is consistent with real-world motion in the scene. The result of our system is that static objects are correctly identified as one segment, even if they are at different depths. Color features and information from previous frames in the video sequence are used to correct occasional errors due to the orientation-based segmentation. We present results on more than thirty videos from different benchmarks. The system is particularly robust on complex background scenes containing objects at significantly different depths.