On The Potential of Image Moments for Medical Diagnosis

Medical imaging is widely used for diagnosis and postoperative or post-therapy monitoring. The ever-increasing number of images produced has encouraged the introduction of automated methods to assist doctors or pathologists. In recent years, especially after the advent of convolutional neural networks, many researchers have focused on this approach, considering it to be the only method for diagnosis since it can perform a direct classification of images. However, many diagnostic systems still rely on handcrafted features to improve interpretability and limit resource consumption. In this work, we focused our efforts on orthogonal moments, first by providing an overview and taxonomy of their macrocategories and then by analysing their classification performance on very different medical tasks represented by four public benchmark data sets. The results confirmed that convolutional neural networks achieved excellent performance on all tasks. Despite being composed of much fewer features than those extracted by the networks, orthogonal moments proved to be competitive with them, showing comparable and, in some cases, better performance. In addition, Cartesian and harmonic categories provided a very low standard deviation, proving their robustness in medical diagnostic tasks. We strongly believe that the integration of the studied orthogonal moments can lead to more robust and reliable diagnostic systems, considering the performance obtained and the low variation of the results. Finally, since they have been shown to be effective on both magnetic resonance and computed tomography images, they can be easily extended to other imaging techniques

GPU-Accelerated Algorithm to Compute Bessel-Fourier Moments

Bessel-Fourier moments have been applied in image pattern reconstruction since their introduction in 2010. In this research, a scalable GPU-based algorithm is proposed to accelerate the computation of Bessel-Fourier moments of high orders while preserving accuracy. To analyze our new algorithm, image reconstructions from Bessel-Fourier moments of orders up to 1000 were tested on two systems. The experimental results prove the correctness and scalability of the algorithm. In addition, by investigating the precision-related performance, both 64-bit and 32-bit precisions were shown to provide the same level of computational accuracy for Bessel-Fourier moments of orders up to 1000. Nevertheless, reconstructions with 64-bit precision are computationally more costly. Furthermore, we applied filtering in Bessel-Fourier moments and Fourier Frequency domains and found that Bessel-Fourier moments share some similarities with the frequencies in Fourier Frequency domain, though more image power is distributed in the Bessel-Fourier moments of lower orders.Master of Science in Applied Computer Scienc

Fast generic polar harmonic transforms

International audienceGeneric polar harmonic transforms have recently been proposed to extract rotation-invariant features from images and their usefulness has been demonstrated in a number of pattern recognition problems. However, direct computation of these transforms from their definition is inefficient and is usually slower than some efficient computation strategies that have been proposed for other methods. This paper presents a number of novel computation strategies to compute these transforms rapidly. The proposed methods are based on the inherent recurrence relations among complex exponential and trigonometric functions used in the definition of the radial and angular kernels of these transforms. The employment of these relations leads to recursive and addition chain-based strategies for fast computation of harmonic function-based kernels. Experimental results show that the proposed method is about 10× faster than direct computation and 5× faster than fast computation of Zernike moments using the q-recursive strategy. Thus, among all existing rotation-invariant feature extraction methods, polar harmonic transforms are the fastest

Fast Computation of Orthogonal Polar Harmonic Transforms

International audienceThis paper presents a method for the computation of polar harmonic transforms that is fast and efficient. The method is based on the inherent recurrence relations among harmonic functions that are used in the definitions of the radial and angular kernels of the transforms. The employment of these relations leads to recursive strategies for fast computation of harmonic function-based kernels. Polar harmonic transforms were recently proposed and have shown nice properties for image representation and pattern recognition. The proposed method is 10-time faster than direct computation and five-time faster than fast computation of Zernike moments

Robust similarity registration technique for volumetric shapes represented by characteristic functions

This paper proposes a novel similarity registration technique for volumetric shapes implicitly represented by their characteristic functions (CFs). Here, the calculation of rotation parameters is considered as a spherical crosscorrelation problem and the solution is therefore found using the standard phase correlation technique facilitated by principal components analysis (PCA).Thus, fast Fourier transform (FFT) is employed to vastly improve efficiency and robustness. Geometric moments are then used for shape scale estimation which is independent from rotation and translation parameters. It is numericallydemonstrated that our registration method is able to handle shapes with various topologies and robust to noise and initial poses. Further validation of our method is performed by registering a lung database

Analysis of the image moments sensitivity for the application in pattern recognition problems

Momenti slike su numerički deskriptori koji sadrže informaciju o svojstvima invarijantnim na translaciju, rotaciju, promjenu skale i neke oblike distorzije, a njihova analiza je jedna od metoda koje se često koriste pri analizi slika i raspoznavanju uzoraka. U okviru ove radnje razvijeni su algoritmi za računanje geometrijskih, Legendreovih, Zernikeovih, Fourier – Mellinovih te tri tipa Fourier – Jacobijevih momenata, kao i iz njih definiranih invarijanti slike u programskom jeziku MatLab uz rješavanje inverznog problema rekonstrukcije početnog ulaza. Za sve tipove momenata osim najjednostavnijih geometrijskih definirani su vektori osjetljivosti na rotaciju i promjenu skale čije su komponente oni članovi skupa koji nose značajnije informacije o ulaznoj slici. Primjenom novih deskriptora na klasifikaciju rukom pisanih slova i identifikacijskih fotografija osoba pokazano je da je relevantna informacija o ulazu na taj način sačuvana, a njihov je izračun znatno brži i jednostavniji uz zadržanu sposobnost jednoznačnog raspoznavanja uzoraka. Korištenjem momenata slike i vektora osjetljivosti analizirani su znakovi s dvaju glagoljskih spomenika te utvrđeno postojanje mješavine znakova trokutastog i okruglog modela glagoljice. Metoda je primijenjena i na klasifikaciju tragova puzanja ličinki mutanata vinske mušice za potrebe proučavanja odgovora živčanog sustava na različite podražaje.Image moments are numerical descriptors invariant to translation, rotation, change of scale and some types of image distortion and their analysis is one of the most often used methods in image processing and pattern recognition. In this work, algorithms for calculation of geometric, Legendre, Zernike, Fourier – Mellin and three types of Fourier – Jacobi moments were implemented in MatLab. Hu's, affine and blur invariants were also obtained as well as inverse problem of input image reconstruction solved. For each type of image moments exept geometric ones the set of sensitivity vectors for rotation and scale were defined. Their components are those image moments which describe more important features of the input image. These new descriptors were applied for classification of handwritten letters and identifying personal photos. It was shown that the process of such descriptor calculation is much faster and simpler while preserving all the relevant information about input image. Using this method, the signs carved in two glagolitic inscriptions were analyzed and the mixture of triangular and round glagolitic letters found. The method was also applied to classification of the mutant fruit fly larvae crawling trails which is needed in studying responses of the nervous system to different stimuli

Generic polar harmonic transforms for invariant image representation

International audienceThis paper introduces four classes of rotation-invariant orthogonal moments by generalizing four existing moments that use harmonic functions in their radial kernels. Members of these classes share beneficial properties for image representation and pattern recognition like orthogonality and rotation-invariance. The kernel sets of these generic harmonic function-based moments are complete in the Hilbert space of square-integrable continuous complex-valued functions. Due to their resemble definition, the computation of these kernels maintains the simplicity and numerical stability of existing harmonic function-based moments. In addition, each member of one of these classes has distinctive properties that depend on the value of a parameter, making it more suitable for some particular applications. Comparison with existing orthogonal moments defined based on Jacobi polynomials and eigenfunctions has been carried out and experimental results show the effectiveness of these classes of moments in terms of representation capability and discrimination power