Abstract Blur is an image degradation that makes object recognition challenging. Restoration approaches solve this problem via image deblurring, deep learning methods rely on the augmentation of training sets. Invariants with respect to blur offer an alternative way of describing and recognising blurred images without any deblurring and data augmentation. In this paper, we present an original theory of blur invariants. Unlike all previous attempts, the new theory requires no prior knowledge of the blur type. The invariants are constructed in the Fourier domain by means of orthogonal projection operators and moment expansion is used for efficient and stable computation. Applying a general substitution rule, combined invariants to blur and spatial transformations are easy to construct and use. Experimental comparison to Convolutional Neural Networks shows the advantages of the proposed theory.

Deep neural networks have recently thrived on single image depth estimation. That being said, current developments on this topic highlight an apparent compromise between accuracy and network size. This work proposes an accurate and lightweight framework for monocular depth estimation based on a self-attention mechanism stemming from salient point detection. Specifically, we utilize a sparse set of keypoints to train a FuSaNet model that consists of two major components: Fusion-Net and Saliency-Net. In addition, we introduce a normalized Hessian loss term invariant to scaling and shear along the depth direction, which is shown to substantially improve the accuracy. The proposed method achieves state-of-the-art results on NYU-Depth-v2 and KITTI while using 3.1-38.4 times smaller model in terms of the number of parameters than baseline approaches. Experiments on the SUN-RGBD further demonstrate the generalizability of the proposed method.

The paper presents a new theory of combined moment invariants to Gaussian blur and spatial affine transformation. The blur kernel may be arbitrary oriented, scaled and elongated. No prior information about the kernel parameters and about the underlaying affine transform is required. The main idea, expressed by the Substitution Theorem, is to substitute pure blur invariants into traditional affine moment invariants. Potential applications of the new descriptors are in blur-invariant image recognition and in robust template matching.

We present a method to reconstruct a dense spatiotemporal depth map of a non-rigidly deformable object directly from a video sequence. The estimation of depth is performed locally on spatio-temporal patches of the video, and then the full depth video of the entire shape is recovered by combining them together. Since the geometric complexity of a local spatiotemporal patch of a deforming non-rigid object is often simple enough to be faithfully represented with a parametric model, we artificially generate a database of small deforming rectangular meshes rendered with different material properties and light conditions, along with their corresponding depth videos, and use such data to train a convolutional neural network. We tested our method on both synthetic and Kinect data and experimentally observed that the reconstruction error is significantly lower than the one obtained using conventional non-rigid structure from motion approaches.

In this paper, we propose a new theory of invariants to Gaussian blur. We introduce a notion of a primordial image as a canonical form of all Gaussian blur-equivalent images. The primordial image is defined in spectral domain by means of projection operators. We prove that the moments of the primordial image are invariant to Gaussian blur and we derive recursive formulas for their direct computation without actually constructing the primordial image itself. We show how to extend their invariance also to image rotation. The application of these invariants is in blur-invariant image comparison and recognition. In the experimental part, we perform an exhaustive comparison with two main competitors: 1) the Zhang distance and 2) the local phase quantization.

In this letter, we propose a global method for registering color images with respect to translation. Our approach is based on the idea of representing translations as convolutions with unknown shifted delta functions, and performing Wiener deconvolution in order to recover the shift between two images. We then derive a quaternionic version of the Wiener deconvolution filter in order to register color images. The use of Wiener filter also allows us to explicitly take into account the effect of noise. We prove that the well-known algorithm of phase correlation is a special case of our method, and we experimentally demonstrate the advantages of our approach by comparing it to other known generalizations of the phase correlation algorithm.

In this paper, we extend our recent registration method designed specifically for registering blurred images. The original method works for unknown blurs, assuming the blurring point-spread function (PSF) exhibits an N -fold rotational symmetry. Here, we also generalize the theory to the case of dihedrally symmetric blurs, which are produced by the PSFs having both rotational and axial symmetries. Such kind of blurs are often found in unfocused images acquired by digital cameras, as in out-of-focus shots the PSF typically mimics the shape of the shutter aperture. This makes our registration algorithm particularly well-suited in applications where blurred image registration must be used as a preprocess step of an image fusion algorithm, and where common registration methods fail, due to the amount of blur. We demonstrate that the proposed method leads to an improvement of the registration performance, and we show its applicability to real images by providing successful examples of blurred image registration followed by depth-of-field extension and multichannel blind deconvolution.

In this paper, we propose a new registration method designed particularly for registering differently blurred images. Such a task cannot be successfully resolved by traditional approaches. Our method is inspired by traditional phase correlation, which is now applied to certain blur-invariant descriptors instead of the original images. This method works for unknown blurs assuming the blurring PSF exhibits an N-fold rotational symmetry. It does not require any landmarks. We have experimentally proven its good performance, which is not dependent on the amount of blur. In this paper, we explicitly address only registration with respect to translation, but the method can be readily generalized to rotation and scaling.