Affine Invariant Mathematical Morphology Applied to A Generic Shape Recognition Algorithm

We design a generic contrast and affine invariant planar shape recognition algorithm. By generic, we mean an algorithm which delivers a list of all shapes two digital images have in common, up to any affine transform or contrast change. Affine invariance must not be considered as a weak requirement in shape recognition since it is well known that if 3D objects with smooth boundaries are being observed, then the deformation of the objects’ images, far enough from the occlusion boundaries, is locally an affine transform. We define as ”shape elements” all pieces of level lines of the image. We then discuss an efficient local encoding of the shape elements. We finally show experiments. Applications aimed at include image registration, image indexing, optical flow.

With the increasing number of available digital images, there is an urgent need of image content description to facilitate content based image retrieval (CBIR). Besides colour and texture, shape is an important low level feature in describing image content. An object can be photographed from different distances and angles. However, we often want to classify the images of the same object into one class, despite the change of perspective. So, it is desired to extract shape features that are invariant to the change of perspective. The shape of an object from one viewpoint to another can be linked through an affine transformation, if it is viewed from a much larger distance than its size along the line of sight. Those invariant shape features are known as affine invariant shape representations. Because of the change of perspective, it is more difficult to develop affine invariant shape representations than normal ones. The goal of this work is to develop affine invariant shape descriptors. Through shape retrieval experiments, we find that the performance of the existing affine invariant shape representations are not satisfactory. Especially, when the shape boundary is corrupted by noise, their performance degrades quickly. In this work, two new affine invariant contour-based shape descriptors, the ICA Fourier shape descriptor (ICAFSD) and the whitening Fourier shape descriptor (WFSD) have been developed. They perform better than most of the existing affine invariant shape representations, while having compact feature size and low computational time requirement. Four region-based affine-invariant shape descriptors, the ICA Zernike moment shape descriptor (ICAZMSD), the whitening Zernike moment shape descriptor (WZMSD), the ICA orthogonal Fourier Mellin moment shape descriptor (ICAOFMMSD), and the whitening orthogonal Fourier Mellin moment shape descriptor (WOFMMSD), are also proposed, in this work. They can be applied to both simple and complex shapes, and have close to perfect performance in retrieval experiments. The advantage of those newly proposed shape descriptors is even more apparent in experiments on shapes with added boundary noise: Their performance does not deteriorate as much as the existing ones.

With the increasing number of available digital images, there is an urgent need of image content description to facilitate content based image retrieval (CBIR). Besides colour and texture, shape is an important low level feature in describing image content. An object can be photographed from different distances and angles. However, we often want to classify the images of the same object into one class, despite the change of perspective. So, it is desired to extract shape features that are invariant to the change of perspective. The shape of an object from one viewpoint to another can be linked through an affine transformation, if it is viewed from a much larger distance than its size along the line of sight. Those invariant shape features are known as affine invariant shape representations. Because of the change of perspective, it is more difficult to develop affine invariant shape representations than normal ones. The goal of this work is to develop affine invariant shape descriptors. Through shape retrieval experiments, we find that the performance of the existing affine invariant shape representations are not satisfactory. Especially, when the shape boundary is corrupted by noise, their performance degrades quickly. In this work, two new affine invariant contour-based shape descriptors, the ICA Fourier shape descriptor (ICAFSD) and the whitening Fourier shape descriptor (WFSD) have been developed. They perform better than most of the existing affine invariant shape representations, while having compact feature size and low computational time requirement. Four region-based affine-invariant shape descriptors, the ICA Zernike moment shape descriptor (ICAZMSD), the whitening Zernike moment shape descriptor (WZMSD), the ICA orthogonal Fourier Mellin moment shape descriptor (ICAOFMMSD), and the whitening orthogonal Fourier Mellin moment shape descriptor (WOFMMSD), are also proposed, in this work. They can be applied to both simple and complex shapes, and have close to perfect performance in retrieval experiments. The advantage of those newly proposed shape descriptors is even more apparent in experiments on shapes with added boundary noise: Their performance does not deteriorate as much as the existing ones.

In this paper, a novel technique for matching images of object shapes which have been subject to affine transformation caused by variations in the camera position is reported. The method is based on the genetic algorithm, and is more efficient and reliable than conventional approaches that rely on corresponding dominant point pairs to determine the best alignment between object boundaries. Experimental results are presented to demonstrate the feasibility of the approach and its capability in identifying object shapes that had been distorted with heavy noise contamination

The major challenges in automatic multi-sensor image registration are the inconsistency in intensity or contrast patterns, and the existence of partial or missing information between images. Here we propose a novel image registration method based on local phase coherence features, which are insensitive to changes in intensity or contrast. Furthermore, a new objective function based on weighted mutual information is proposed, where less weight is given to the objects that have no correspondence between images. The proposed method has been tested on both synthetic and medical images and evaluated based on registration accuracy. Our experiments demonstrate good performance of the proposed approach with missing or partial data, with significant changes in contrast, and with the presence of noise.

Digital image interpretation by analysis of image-image correspondence

Digital image metadata plays a crucial role in managing digital image repositories. It lets us catalog and maintain large image collections as well as search for and find relevant information. Moreover, describing a digital image with defined metadata schemes lets multiple systems with different platforms and interfaces access and process image metadata. Metadata's wide use in commercial, academic, and educational domains as well as on the Web has propelled the development of new standards for digital image data schemes. The Japan Electronics and Information Technology Industries Association has proposed the Exchangeable Image File Format (EXIF) as a standard for storing administrative metadata in digital image files during acquisition. The International Press Telecommunications Council (IPTC) has developed a standard for storing descriptive metadata information within digital images. These metadata schemas, as well as other emerging standards, provide a standard format for creating, processing, and exchanging digital image metadata and enable image management, analysis, indexing, and search applications.

Leaf Area Index (LAI) and biomass (BIO) are essential agronomic parameters that reflect the growth of potatoes and are related to their biomass. Their precise estimation is capable of monitoring crop growth, guiding field management, and optimizing planting spatial patterns. Traditional potato leaf area indexing and biomass estimation primarily rely on field sampling surveys. This method is low in efficiency, high in cost, and limited by the number of samples. It cannot accurately reflect potato growth and meet the real-time estimation needs of large areas. Compared to the use of satellite remote sensing data (RSD) for estimating LAI and biomass, research on estimating these two phenotypic parameters using crewless aerial vehicle (UAV) RSD is relatively immature. Research on estimating crop growth index parameters by remote sensing primarily focuses on data obtained from specific types of sensors, targeting specific growth stages to compare and analyze the accuracy of different methods. However, there are few estimates of the impact of optimizing the best data types and optimal growth stage for LAI and biomass estimation by comparing and analyzing different sensor data and different growth stages. Multi-sensor integration technology has made it possible to study different crop phenotype information and estimate the best data type and optimal growth stage in crop phenotypic data estimation, establishing it as a new hot spot in the field. This paper integrates high-definition digital cameras and imaging hyperspectrometers on the UAV platform to obtain digital images and hyperspectral data simultaneously, along with ground-measured potato leaf area index and biomass data. Using the partial least squares regression (PLSR), random forest (RF), support vector machine (SVM), and backpropagation (BP) neural network methods, we got digital images and hyperspectral data from different stages of growth, put together a digital image index and a vegetation index, and looked at how they related to LAI and BIO. Then, we chose the index that had the strongest correlation. To establish LAI and biomass estimation models at various growth phases, this paper compared and analyzed the estimation impacts of various data types and models at various growth phases. It then selected the best data types for LAI estimation and biomass estimation at different growth stages, as well as the best growth phases for LAI and biomass estimation. The outcomes indicated that when potato LAI was estimated, the mean values of R 2 and RMSE of the four estimation models were 0.75 and 0.30 Kg/mu at the tuber growth stage, respectively, and the estimation effect was the best, indicating that this was the best growth phase for LAI estimation. The average values of R 2 and RMSE in the LAI estimation model using the hyperspectral vegetation index were 0.73 and 0.33 Kg/mu, respectively, indicating that hyperspectral data was the best data type for LAI estimation. When potato biomass was estimated, the mean values of R 2 and RMSE of the four methods were 0.67 and 15.25 Kg/mu, respectively, at the tuber growth stage, which were better than other growth phases, demonstrating that this was the best growth phase for biomass estimation. The average values of R 2 and RMSE of the biomass estimation model using the hyperspectral vegetation index were 0.67 and 20.08 Kg/mu, respectively, indicating that the hyperspectral data was the best data type for biomass estimation. The average values of R 2 of the LAI and biomass estimation model at the maturity stage were only 0.56 and 0.36, both of which indicated poor estimation effects. Our study can serve as a guide to selecting the most effective method for estimating parameters for essential indexes in crop growth monitoring.

Content-based indexing of images consists in extracting visual information from digital images (such as pixels, colors, objects, shapes, etc.), and can be performed automatically and fast by computers. This work focuses on color indexing of images. A statistical algorithm called Mean-Shift is used to modelize the color distributions of images as two-dimensional Gaussian kernels. The experiments have been performed on the COIL1 database and the results show that the proposed method compares well to other content-based retrieval methods.

The moiré effect and phenomena are natural occurring geometric formations that appear during the super-position of grid structures. Most widely recognisable in colour printing practices, generally viewed on screens (computer and TV) they are in most cases examples of interference within a signal or a code, unwanted visual mis-alignment. Especially in digital image capture, moiré patternings appear when a geometrically even pattern, like a fabric or close-up of fine texture, has an appearance of rippled water with blue or red hues of concentric circle formations. The intriguing pattern formation in this case points back not only to the mis-alignment of frequencies, but can be further seen as the intersection point of a speculative ontology for the index of the digital image. Moiré not only as a visually reproducible phenomenon or effect, but a field of vision that blurs the boundaries between analogue and digital, perception and affect, manifesting the photographic as a constant site of becoming, a site of immanence. The philosophy of Henri Bergson, Brian Massumi and Francois Laruelle will be explored alongside the moiré image and phenomenon, to see if there is such a speculative site underlining the becoming of the digital image and its repercussions in contemporary digital culture.

Patches are small images (typically $8\times 8$ to $12\times 12$) extracted from natural images. The ``patch space'' is the set of all observable patches extracted from digital images in the world. This observable space is huge and should permit a sophisticated statistical analysis. In the past ten years, statistical inquiries and applications involving the ``patch space'' have tried to explore its structure on several levels. The first attempts have invalidated models based on PCA or Fourier analysis. Redundant bases (or patch dictionaries) obtained by independent component analysis (ICA) or related processes have tried to find a reduced set of patches on which every other patch obtains a sparse decomposition. Optimization algorithms such as EM have been used to explore the patch space as a Gaussian mixture. The goal of the present paper is to review this literature, and to extend its methodology to gain more insight on the independent components of the patch space.  &nbsp The conclusion of our analysis is that the sophisticated ICA tools introduced to analyze the patch space require a previous geometric normalization step to yield non trivial results. Indeed, we demonstrate by a simple experimental setup and by the analysis of the literature that, without this normalization, the patch space structure is actually hidden by the rotations, translations, and contrast changes. Thus, ICA models applied on a random set of patches boil down to segmenting the patch space depending on insignificant dimensions such as the patch orientation or the position of its gradient barycenter. When, instead of exploring the raw patches, one decides to explore the quotient of the set of patches by these action groups, a geometrically interpretable patch structure is revealed.

We address the problem of texture segmentation by using a novel affine invariant model. The introduction of affine invariance as a requirement for texture analysis goes beyond what is known of the human performance and also beyond the psychophysical theories. We propose to compute texture features using affine invariant intrinsic neighborhoods and affine invariant intrinsic orientation matrices. We discuss several possibilities for the definition of the channels and give comparative experimental results where an affine invariant Mumford-Shah type energy functional is used to compute the multichannel affine invariant segmentation. We prove that the method is able to retrieve faithfully the texture regions and to recover the shape from texture information in images where several textures are present. The numerical algorithm is multiscale.

Digital image recognition based on Fractional-order-PCA-SVM coupling algorithm

Partial differential equations and mathematical morphology

In tissue counter analysis, digital images are overlayed with regularly distributed measuring masks (elements) of equal size and shape, and the digital contents (grey level, colour and texture parameters) of each element are used for statistical analysis. In this study we assessed the applicability of tissue counter analysis and machine learning algorithms on tumour segmentation and diagnostic discrimination of benign and malignant melanocytic skin lesions. A total of 369 standardised dermatoscopic images (93 melanomas, 276 benign nevi) were evaluated. The Classification and Regression Tree (CART) analysis was performed in order to differentiate between melanocytic skin lesions and surrounding skin. Instance-based learning (1-NN) was tested for differentiating between benign and malignant tumour elements. For diagnostic assessment, only the percentage of elements suggestive for malignancy in each lesion was used. Evaluation of a total of 369 melanocytic skin lesions showed a suitable segmentation of the tumour portion in 97.6%. When instance-based learning was applied to an independent test set, a threshold value of 27.4% of elements suggestive for malignancy recognised 35 out of 35 melanomas and 100 out of 101 nevi (sensitivity 100%, specificity 99%, positive predictive value 97.2%, negative predictive value 100%). Tissue counter analysis combined with machine learning algorithms turned out to be a useful method for diagnostic purposes in epiluminescence microscopy.