Modification to first-order Born approximation for improved prediction of scattered sound from weakly scattering objects

When deriving the Fourier diffraction theorem based on the first-order Born approximation,the difference between wave number of the scattering object and that of the surrounding medium is ignored,causing substantial errors in sound scattering prediction.This paper modifies the Born approximation by taking into account the amplitude and phase changes between the scattering object and the water due to the wave number difference.By changing the radius and center position of the sampling circle in the Fourier domain,accuracy of the predicted sound scattering is improved.With the modified Born approximation,the computed far-field directional pattern of the scattered sound from a circular cylinder is in good agreement with the rigorous solution.Numerical calculations for several objects with different shapes are used to show applicability and effectiveness of the proposed method.

Weakly Supervised Object Localization with Background Suppression Erasing for Art Authentication and Copyright Protection

The problem of art forgery and infringement is becoming increasingly prominent,since diverse self-media contents with all kinds of art pieces are released on the Internet every day.For art paintings,object detection and localization provide an efficient and ef-fective means of art authentication and copyright protection.However,the acquisition of a precise detector requires large amounts of ex-pensive pixel-level annotations.To alleviate this,we propose a novel weakly supervised object localization(WSOL)with background su-perposition erasing(BSE),which recognizes objects with inexpensive image-level labels.First,integrated adversarial erasing(IAE)for vanilla convolutional neural network(CNN)dropouts the most discriminative region by leveraging high-level semantic information.Second,a background suppression module(BSM)limits the activation area of the IAE to the object region through a self-guidance mechanism.Finally,in the inference phase,we utilize the refined importance map(RIM)of middle features to obtain class-agnostic loc-alization results.Extensive experiments are conducted on paintings,CUB-200-2011 and ILSVRC to validate the effectiveness of our BSE.

Shallow Feature-driven Dual-edges Localization Network for Weakly Supervised Localization

Weakly supervised object localization mines the pixel-level location information based on image-level annotations.The traditional weakly supervised object localization approaches exploit the last convolutional feature map to locate the discriminative regions with abundant semantics.Although it shows the localization ability of classification network,the process lacks the use of shallow edge and texture features,which cannot meet the requirement of object integrity in the localization task.Thus,we propose a novel shallow feature-driven dual-edges localization(DEL)network,in which dual kinds of shallow edges are utilized to mine entire target object regions.Specifically,we design an edge feature mining(EFM)module to extract the shallow edge details through the similarity measurement between the original class activation map and shallow features.We exploit the EFM module to extract two kinds of edges,named the edge of the shallow feature map and the edge of shallow gradients,for enhancing the edge details of the target object in the last convolutional feature map.The total process is proposed during the inference stage,which does not bring extra training costs.Extensive experiments on both the ILSVRC and CUB-200-2011 datasets show that the DEL method obtains consistency and substantial performance improvements compared with the existing methods.

Categorical resolutions of a class of derived categories

We clarify the relation between the subcategory D_(hf)~b(A) of homological finite objects in D^b(A)and the subcategory K^b(P) of perfect complexes in D^b(A), by giving two classes of abelian categories A with enough projective objects such that D_(hf)~b(A) = K^b(P), and finding an example such that D_(hf)~b(A)≠K^b(P). We realize the bounded derived category D^b(A) as a Verdier quotient of the relative derived category D_C^b(A), where C is an arbitrary resolving contravariantly finite subcategory of A. Using this relative derived categories, we get categorical resolutions of a class of bounded derived categories of module categories of infinite global dimension.We prove that if an Artin algebra A of infinite global dimension has a module T with inj.dimT <∞ such that ~⊥T is finite, then D^b(modA) admits a categorical resolution; and that for a CM(Cohen-Macaulay)-finite Gorenstein algebra, such a categorical resolution is weakly crepant.