In this paper, we obtain two intrinsic integral inequalities of Hessian manifolds.

While many real-world optimization problems typically involve multiple constraints, unconstrained problems hold practical and fundamental significance. They can arise directly in specific applications or as transformed versions of constrained optimization problems.‎ ‎Newton's method‎, ‎a notable numerical technique within the category of line search algorithms, is widely used for function optimization‎. The search direction and step length play crucial roles in this algorithm. ‎This paper introduces an algorithm aimed at enhancing the step length within the Broyden quasi-Newton process‎. ‎Additionally‎, ‎numerical examples are provided to compare the effectiveness of this new method with another approach‎.

Reliable image matching is a vital step in many photogrammetric processes. Most image matching methods are based on the local feature algorithms because of their robustness to significant geometric and radiometric differences. A local feature is generally defined as a distinct structure with properties differing from its immediate neighbourhood. Generally, local-feature-based image matching methods consist of three main steps, including feature detection, feature description and feature correspondence. In the feature detection step, distinctive structures are extracted from images. In the feature description step, extracted features are represented with descriptors to characterize them. Finally in the correspondence step, the extracted features from two images are matched using particular similarity measures.n this paper, an automatic image matching approach based on the affine invariant features is proposed for wide-baseline images with significant viewpoint differences. The proposed approach consists of three main steps. In the first step, well-known Hessian-affine feature detector is used to extract local affine invariant features in the image pair. In Hessian-affine detector a multi-scale representation and an iterative affine shape adaption are used to deal with significant viewpoint differences including large scale changes. To improve the Hessian-affine detector capability, an advanced strategy based on the well-known UR-SIFT (uniform robust scale invariant feature transform) algorithm is applied to extract effective, robust, reliable, and uniformly distributed elliptical local features. For this purpose, a selection strategy based on the stability and distinctiveness constraints is used in the full distribution of the location and the scale.In the second step, a distinctive descriptor based on MROGH (Multisupport Region Order-Based Gradient Histogram) method, which is robust to significant geometrical distortions, is generated for each extracted feature. The main idea of the MROGH method is to pool rotation invariant local features based on intensity orders. Instead of assigning a main orientation to each feature, a locally rotation invariant schema is used. For this purpose a rotation invariant coordinate system is used to compute the pixels gradient. To compute descriptor, the pixels in the feature region are partitioned into several groups based on their intensity orders. Then, a specific histogram based on the pixels gradient magnitude and orientation is calculated for each group. Finally, the MROGH descriptor is generated by combining the values of all the gradient histogram from all groups into a single feature vector.Finally, feature correspondence and blunder detection process is performed using epipolar geometry based on fundamental matrix. The initial matched features that are not consistent with the estimated fundamental matrix are identified as false matches and eliminated. A distance threshold TE=1 pixel between each feature point and its epipolar line is considered as elimination condition. The experimental results using six close-range images show that the proposed method improves the matching performance compared with several state-of-the-art methods, including the MSER-SIFT, UR-SIFT and A-SIFT, in terms of the number of correct matched features, recall and positional accuracy. Based on the matching results, the proposed integrated method can be easily applied to a variety of photogrammetric and computer vision applications such as relative orientation, bundle adjustment, structure from motion and simultaneous localization and mapping (SLAM).

Sufficient conditions for the boundedness and regularity of a function, whose partial derivatives satisfy a certain set of equations, are presented. Energy methods are used to establish these results. The asymptotic behavior of the gradient toward a constant function is also investigated.

We present sufficient conditions for boundedness and regularity of a function whose partial derivatives satisfy a certain set of equations. We use energy methods to establish these results. We also investigate asymptotic behavior of the gradient toward a constant function.

In this paper, we present an edge detection method based on wavelet transform and Hessian matrix of image at each pixel. Many methods which based on wavelet transform, use wavelet transform to approximate the gradient of image and detect edges by searching the modulus maximum of gradient vectors. In our scheme, we use wavelet transform to approximate Hessian matrix of image at each pixel, too. The main idea of our methods lies in the fact that, the direction of largest surface curvature is the eigenvector of the Hessian matrix corresponding to the largest absolute eigenvalue. Infact, we use the Hessian matrix's information to increase or decrease the effect of wavelet transform in and directions.

Feature selection is one of the most important techniques in machine learning and pattern recognition, which eliminates redudant features and selects a suitable subset of features. This avoids overfitting when building the model and improves the model performance. In many applications, obtaining labeled data is costly and time consuming, while unlabeled data are readily available. Therefore, semi-supervised feature selection methods can be used to consider both labeled and unlabeled data in the feature selection process. In this paper, a semi-supervised sparse feature selection method is proposed based on hessian regularization and Fisher discriminant analysis which selects the appropriate features using the labeled data and the local structure of both labeled and unlabeled data. In the proposed method, an objective function based on semi-supervised scatter matrix and l2,1-norm is presented for feature selection which considers the correlation among features. To solve the proposed objective function, an iterative algorithm is used and its convergence is experimentally and theoretically proved. The results of the experiments on five data sets indicate that the proposed method improves the selection of relevant features compared to other methods used in this paper.

Mayetiola destructor (Say, 1817) originated in the Fertile Crescent region of the Middle East and is one of the most serious pests of wheat, rye and barley and more than 16 Poaceae wild species. Here, we report the occurrence of this species as an invasive pest for the first time in Iran. It was detected in wheat fields and rye in Qüshchï Pass, Urmia environ, West Azarbaijan province (September 2020) as well as in wheat fields in Bil-e Savar, Ardabil province (July 2024). The diagnostic characters and its life history as well as the photographs of the adult male and female, larvae, puparium, male genitalia and wing venation are provided. This is the second species from the genus Mayetiola that has been reported from Iran. To prevent the spread of this destructive pest in Iran, suitable management practices are urgently needed.

In this article, the history of matrix and determinants from the beginning to the beginning of the 20th century is studied. But in the 20th century, the theory of matrices has spread so much that writing a history about it will probably be very voluminous and a separate history should be written for each of the topics. The fact that the Gaussian elimination method has a history of more than 2000 years is one of the points we will address. We want to know by whom matrices were introduced and developed before the 20th century. We will also introduce the first person who used determinants and study his influence on the work of later mathematicians. Today, matrices are expanding, but determinants are not much considered because of the large amount of calculations they have, and the invention of digital computers did not cause us to return to Cramer's method, but at one time, determinants were much more interested than matrices.