Although Convolutional Neural Networks provided effective solutions for computer vision tasks across various domains in recent years, the high training times of the models remain a crucial aspect. A straightforward way to decrease the computational costs is to use smaller images during training. However, existing image resizing approaches are either computationally intensive or lossy methods. This paper introduces the usage of the Cantor pairing function for image resizing through pixel reduction. The pairing function is a fast bijective transformation that maps a pair of two integers into a single value. Combining two pixels into one leads to a decrease in the image size, while the bijective property ensures a lossless transformation. The experiments conducted on the MNIST datasets demonstrated that the proposed approach reduces resizing time at least six times, decreases training times significantly, and achieves similar performance with baseline methods.
Curve-thinning is an iterative reduction to extract centerlines from binary/segmented objects. Parallel thinning algorithms are composed of parallel reductions, and the fully parallel approach uses the same parallel reduction in each thinning phase. This paper presents the first fully parallel 3D curve-thinning algorithm acting on the unconventional face-centered cubic (FCC) grid. Our algorithm combines a sufficient condition for topology-preserving parallel reductions acting on (18, 12) pictures of the FCC grid with curve-endpoint preservation, hence its topological correctness is guaranteed for all possible pictures. In order to reduce the count of unwanted side branches in the produced centerlines, a novel iteration-level endpoint re-checking process is proposed.
Thinning algorithms consist of iterative object reduction steps, which are repeated until stability is reached. In each iteration step, a set of points in the outermost layer of the current object is investigated for possible deletion. In the concept of a k-attempt version of a thinning algorithm, any object point is investigated at most k-times ( k = 1, 2,… ). If a point “survives” the deletion attempts k times, then it is considered as an element of the produced centerline and not investigated anymore. This concept yields a faster thinning approach; however, the result may not be the same as we could get without any limitation of deleting attempts. In this work, we compare a set of existing thinning algorithms without any restriction of deletion attempts and their k-attempt versions. Our aim with this is twofold. We would like to investigate that, what the drawback is in the similarity of the k-attempt version of a thinning algorithm regarding the original one. On the other hand, if the k-attempt version of a thinning algorithm produces the same result as the original set of objects, then it is worth investigating the proof in further work.
In this paper we extend a scalar Q-convexity shape descriptor in two ways towards rotational and rotation-free multidirectional descriptors. Since the original descriptor is defined with respect to the horizontal and vertical directions, we increase its ability to represent a shape by repeatedly rotating the shape and computing the descriptor, in the first extension. However, since rotation is generally not a safe transformation in the 2D digital space, as a second approach, we develop an alternative that works directly with an arbitrary pair of orthogonal lattice directions: the shape remains fixed and a certain number of pairs of directions are employed. We provide the algorithmic details of this approach and its computational complexity. In case of both approaches, the Q-concavity values measured along different directions can be gathered into a vector multidirectional descriptor (signature). We conducted experiments on the MPEG-7 dataset with different sets of lattice directions. We conclude that even though the rotational signature is faster to compute, the rotation-free signature can ensure better classification accuracy. Depending on whether computational time or accuracy is more important in the given application, one of the two methods can be preferred to the other, and hence both of them seem to provide a viable option.
In this paper, we investigate a tomography reconstruction approach for binary images on the Cairo pattern. In discrete tomography the underlying grid plays an essential role, as the projection data and the structure of the grid together give the information that we can use for the reconstruction purpose. The Cairo pattern is one of the most known pentagonal tessellations of the plane and it has a nice symmetric structure for orthogonal projections giving the information in a somewhat different way as similar direction projections on the traditional square grid. We present how gradient based reconstruction method can be used to reconstruct images based on pentagonal pixels in the Cairo pattern. A short experimental evaluation is also presented.
