Supplementary Material: Coarse-to-Fine Segmentation With Shape-Tailored Continuum Scale Spaces
نویسندگان
چکیده
where Î denotes the Fourier transform, and ω denotes frequency. Proof 1 Taking the Fourier transform of the Heat Equation: { ∂tu(t, x) = ∆u(t, x) x ∈ R u(0, x) = I(x) t = 0 yields: ∂tû(t, ω) = (iω) · (iω)û(t, ω) = −|ω|û(t, ω), where û(t, ω) is the Fourier transform of u. Solving this differential equation yields û(t, ω) = e−|ω| 2tÎ(ω). We note that a = 0 when I ∈ L since Î(0) = ∫ R2 I(x) dx is finite. Then by Parseval’s Theorem, E = ∫ ∞
منابع مشابه
Coarse-to-Fine Segmentation With Shape-Tailored Scale Spaces
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 ...
متن کاملA Coarse-to-Fine Human Body Segmentation Method in Video
Human body precise segmentation is difficult because of inter-occlusion when there are multiple human bodies in video. A coarse-to-fine segmentation method is proposed. In coarse segmentation, human shape models are used to get human’s position and coarse region. The human models with variant scale and posture are constructed with head, torso, and legs. For each human body, its corresponding hu...
متن کاملA Space-time Approach to Coupled Atomistic/continuum Simulation
A space-time finite element method employing discontinuous Galerkin approach, for dynamic molecular simulations is proposed. In our approach, a small region of the domain is simulated using fine scale space-time FEM and it is coupled with a coarse scale simulation which employs enriched space-time FEM. The developed approach is motivated by the needs to understand the mechanics and physics that...
متن کاملSingle Image Dehazing via Multi-Scale Convolutional Neural Networks Supplementary Material
Effectiveness of Fine-scale Network: As stated in the manuscript, the finescale network is able to refine the holistic prediction generated by the coarse-scale network. In this supplemental material, we conduct more experiments to show the dehazing results without using fine-scale or coarse-scale networks in Figure 1. We note the architectures of these two networks are similar except input and ...
متن کاملSilhouette-Based Isolated Object Recognition through Curvature Scale Space
Farzin Mokhtarian Abstrac-A complete, fast and practical isolated object recognition system has been developed which is very robust with respect to scale, position and orientation changes of the objects as well as noise and local deformations of shape (due to perspective projection, segmentation errors and nonrigid material used in some objects). The system has been tested on a wide variety of ...
متن کامل