Side information in robust principal component analysis: algorithms and applications

Dimensionality reduction and noise removal are fundamental machine learning tasks that are vital to artificial intelligence applications. Principal component analysis has long been utilised in computer vision to achieve the above mentioned goals. Recently, it has been enhanced in terms of robustness to outliers in robust principal component analysis. Both convex and non-convex programs have been developed to solve this new formulation, some with exact convergence guarantees. Its effectiveness can be witnessed in image and video applications ranging from image denoising and alignment to background separation and face recognition. However, robust principal component analysis is by no means perfect. This dissertation identifies its limitations, explores various promising options for improvement and validates the proposed algorithms on both synthetic and real-world datasets. Common algorithms approximate the NP-hard formulation of robust principal component analysis with convex envelopes. Though under certain assumptions exact recovery can be guaranteed, the relaxation margin is too big to be squandered. In this work, we propose to apply gradient descent on the Burer-Monteiro bilinear matrix factorisation to squeeze this margin given available subspaces. This non-convex approach improves upon conventional convex approaches both in terms of accuracy and speed. On the other hand, oftentimes there is accompanying side information when an observation is made. The ability to assimilate such auxiliary sources of data can ameliorate the recovery process. In this work, we investigate in-depth such possibilities for incorporating side information in restoring the true underlining low-rank component from gross sparse noise. Lastly, tensors, also known as multi-dimensional arrays, represent real-world data more naturally than matrices. It is thus advantageous to adapt robust principal component analysis to tensors. Since there is no exact equivalence between tensor rank and matrix rank, we employ the notions of Tucker rank and CP rank as our optimisation objectives. Overall, this dissertation carefully defines the problems when facing real-world computer vision challenges, extensively and impartially evaluates the state-of-the-art approaches, proposes novel solutions and provides sufficient validations on both simulated data and popular real-world datasets for various mainstream computer vision tasks.Open Acces

Computer vision techniques for modelling the roasting process of coffee (Coffea arabica L.) var. Castillo

[EN] Artificial vision has wide-ranging applications in the food sector; it is easy to use, relatively low cost and allows to conduct rapid non-destructive analyses. The aim of this study was to use artificial vision techniques to control and model the coffee roasting process. Samples of Castillo variety coffee were used to construct the roasting curve, with captured images at different times. Physico-chemical determinations, such as colour, titratable acidity, pH, humidity and chlorogenic acids, and caffeine content, were investigated on the coffee beans. Data were processed by (i) Principal component analysis (PCA) to observe the aggrupation depending on the roasting time, and (ii) partial least squares (PLS) regression to correlate the values of the analytical determinations with the image information. The results allowed to construct robust regression models, where the colour coordinates (L*, a*), pH and titratable acidity presented excellent values in prediction (R-Pred(2) 0.95, 0.91, 0.94 and 0.92). The proposed algorithms were capable to correlate the chemical composition of the beans at each roasting time with changes in the images, showing promising results in the modelling of the coffee roasting process.Supported by the Universidad Surcolombiana, Project No. USCO-VIPS-3050.Ivorra Martínez, E.; Sarria-González, JC.; Girón Hernández, J. (2020). Computer vision techniques for modelling the roasting process of coffee (Coffea arabica L.) var. Castillo. Czech Journal of Food Sciences. 38(6):388-396. https://doi.org/10.17221/346/2019-CJFSS38839638

Controle do estágio de torrefação de café através de técnicas de visão artificial

[EN] Artificial vision techniques were used to evaluate its application in the control of the coffee roasting stage. Coffee samples of Colombia and Castillo varieties were obtained and analyzed by comparing images during the roasting stage. A one-way ANOVA analysis exhibited 94.28% of similarity of the coffee varieties studied; a multivariate analysis showed significant differences (p<0.05) for the time factor and its interaction with the variety factor, no differences were observed (p>0.05) for the coffee varieties. Additionally, a Principal Component, with two components demonstrated 90.77% of the variance by differentiating the samples in the different roasting times. Therefore, the proposed technique could be used in the control of the coffee roasting stage.[PT] Para avaliar o controle do estágio de torrefação de café, foram utilizadas técnicas de visão artificial e variedades de café, Colombia e Castillo, as quais foram analisadas através da comparação de imagens durante a torrefação. A análise de variância mostrou similaridade de 94,28% entre as variedades estudadas. A análise multivariada mostrou diferenças significativas (p<0,05) para o fator tempo e sua interação com o fator variedade, não foram observadas diferenças para as variedades de café (p>0,05). E ainda foi realizada uma análise de componentes principais. Com dois componentes principais, 94,23% da variância foi explicada pela discriminação das amostras nos tempos de torrefação. Ao que se conclui que a técnica proposta pode ser uma ferramenta no controle do estágio de torrefação de café.Sarria-González, JC.; Ivorra Martínez, E.; Girón-Hernández, J. (2019). Control of the coffee roasting stage using artificial vision techniques. Coffee Science (Online). 14(1):33-37. http://hdl.handle.net/10251/163574S333714

Sistem Deteksi Kualitas Buah Jambu Air Berdasarkan Warna Kulit Menggunakan Algoritma Principal Component Analysis (Pca) dan K-Nearest Neigbor (K-NN)

One form of artificial intelligence is the automatic detection of images. so the system can determine precisely the type of image or it can be called computer vision. Water guava fruit is a fruit that is often encountered in Indonesia, but many of the water guavas in the community are of poor quality, thus detrimental to consumers. Therefore we need a system that can detect the quality of the water guava. The Principal Component Analysis (PCA) algorithm and the k-nearest neighbor (k-NN) algorithm can be combined to do this job. PCA is an algorithm that can convert to a group of data that is initially correlated into uncorrelated data (Principal Component). The number of Principal Components generated is the same as the original data, but can be reduced to a smaller amount and is still able to represent the original data well. Meanwhile, k-NN is a method for classifying objects based on learning data that is closest to the object. The research model used in this research is a prototype, and the development tools used are UML. In making the water guava quality detection system, the MATLAB programming language is used, and the test uses the blacbox method. The result of this system is that the system is able to produce output in the form of quality classification of water guava fruit automatically.Keywords: Computer vision, PCA, k-N