Abstract Using the topological equivalence between the Riemann sphere $$\mathbb {S}$$ S and the extended complex plane $$\overline{\mathbb {C}} = \mathbb {C} \cup \{\infty \}$$ C¯=C∪{∞} , where $$\mathbb {C}$$ C is the field of complex numbers, we establish 2D-bijective representations of 3D point clouds. Points of 3D point clouds are mapped into the Riemann sphere $$\mathbb {S}$$ S , and a stereographic projection is implemented to map the points into the complex plane $$\mathbb {C}$$ C . The way the 3D objects are mapped into $$\mathbb {S}$$ S may be varied for various applications. To prove the accuracy and efficiency of the proposed 2D representation of 3D objects, we apply this correspondence to 3D point cloud encryption. We utilize chaotic permutations, chaotic circuits, and Latin cubes in addition to the stereographic projection representation to construct our scheme. The permutation steps using chaotic maps and Latin cubes are carried out on the object data points in both $$\mathbb {S}$$ S and $$\overline{\mathbb {C}}$$ C¯ , while the chaotic circuits are applied to 2D projections of the 3D objects. To the best of our knowledge, no earlier work employed stereographic projections for 3D object encryption. Experimental simulations of this method show high encryption strength and strong confusion and diffusion properties based on quantitative and statistical measures.

Automated classification of HEp-2 cell images is crucial for fast and accurate detection of autoimmune diseases. Recent competitions resulted in high classification rates on publicly available datasets. However, performance on low-resolution HEp-2 images typically lagged behind that of high-resolution images due to the blurring and sub-sampling of fine cellular details. Direct interpolation of low-resolution images couldn't fill in the performance gap. We propose a learning-based approach to infer high-resolution features from low-resolution HEp-2 images. Our approach exploits partial least-square (PLS) to linearly project low- and high-resolution HEp-2 image features into a common linear subspace where the features are highly correlated. Experimental and statistical evaluations show significant improvement in classification performance due to our technique in comparison with direct interpolation and canonical correlation analysis techniques.

This paper proposes a novel approach for sparse coding that further improves upon the sparse representation-based classification (SRC) framework. The proposed framework, Affine-Constrained Group Sparse Coding (ACGSC), extends the current SRC framework to classification problems with multiple input samples. Geometrically, the affineconstrained group sparse coding essentially searches for the vector in the convex hull spanned by the input vectors that can best be sparse coded using the given dictionary. The resulting objective function is still convex and can be efficiently optimized using iterative block-coordinate descent scheme that is guaranteed to converge. Furthermore, we provide a form of sparse recovery result that guarantees, at least theoretically, that the classification performance of the constrained group sparse coding should be at least as good as the group sparse coding. We have evaluated the proposed approach using three different recognition experiments that involve illumination variation of faces and textures, and face recognition under occlusions. Preliminary experiments have demonstrated the effectiveness of the proposed approach, and in particular, the results from the recognition/occlusion experiment are surprisingly accurate and robust.

Consumer-level digital cameras typically post-process raw captured image data to produce enhanced visually appealing output RGB images. Post-processing operations include color gamut compression, tone mapping and other non-linear color corrections. However, raw image data is needed for many computer vision applications such as photometric stereo, shape from shading, and color constancy. Recovering raw image data from RGB images is complicated by the high non-linearity of the post-processing operations. In this paper, we propose a coupled dictionary scheme to model the relationship between the raw and RGB color image spaces of consumer cameras. Dictionary learning is regularized by sparsity constraints on feature representation. As well, we explore a more elaborate variant of coupled dictionary schemes that models the feature coupling more accurately. We test the proposed dictionary learning schemes on many commercial camera datasets. Our experimental results show accurate recovery of raw image data that looks visually indistinguishable from the ground truth.

Recent approaches in image super-resolution suggest learning dictionary pairs to model the relationship between low-resolution and high-resolution image patches with sparsity constraints on the patch representation. Most of the previous approaches in this direction assume for simplicity that the sparse codes for a low-resolution patch are equal to those of the corresponding high-resolution patch. However, this invariance assumption is not quite accurate especially for large scaling factors where the optimal weights and indices of representative features are not fixed across the scaling transformation. In this paper, we propose an augmented coupled dictionary learning scheme that compensates for the inaccuracy of the invariance assumption. First, we learn a dictionary for the low-resolution image space. Then, we compute an augmented dictionary in the high-resolution image space where novel augmented dictionary atoms are inferred from the training error of the low-resolution dictionary. For a low-resolution test image, the sparse codes of the low-resolution patches and the lowresolution dictionary training error are combined with the trained high-resolution dictionary to produce a high-resolution image. Our experimental results compare favourably with the non-augmented scheme.