IEEE Transactions on Image Processing

In this paper, we revisit the analytical expressions of the three Canny's (1983) criteria for edge detection quality: good detection, good localization, and low multiplicity of false detections. Our work differs from Canny's work on two essential points. Here, the criteria are given for discrete sampled signals, i.e., for the real, implemented filters. Instead of a single-step edge as input signal, we use pulses of various width. The proximity of other edges affects the quality of the detection process. This is taken into account in the new expressions of these criteria. We derive optimal filters for each of the criteria and for any combination of them. In particular, we define an original filter which maximizes detection and localization and a simple approximation of the optimal filter for the simultaneous maximization of the three criteria. The upper bounds of the criteria are computed which allow users to measure the absolute and relative performance of any filter (exponential, Deriche (1987), and first derivative of Gaussian filters are evaluated). Our criteria can also be used to compute the optimal value of the scale parameter of a given filter when the resolution of the detection is fixed.

In this correspondence, we prove that the affine invariants, for image registration and object recognition, proposed recently by Yang and Cohen (see ibid., vol.8, no.7, p.934-46, July 1999) are algebraically dependent. We show how to select an independent and complete set of the invariants. The use of this new set leads to a significant reduction of the computing complexity without decreasing the discrimination power.

A theory is presented addressing the fundamental limits of image estimation in a setup that uses two photon-correlated beams. These beams have the property that their photon arrivals, as a point process, are ideally synchronized in time and space. The true image represents the spatial distribution of the optical transmittance (or reflectance) of an object. In this setup, one beam is used to probe the image while the other is used as a reference providing additional information on the actual number of photons impinging on the object. This additional information is exploited to reduce the effect of quantum noise associated with the uncertainty in the number of photons per pixel. A stochastic model for the joint statistics of the two observation matrices is developed and used to obtain a local maximum-likelihood estimator of the image. The model captures the nonideal nature of the correlation between the photons of the beams by means of a simple random translation model. The mean-square error of the estimator is evaluated and compared to the corresponding conventional techniques. Conditions for the performance advantage of the proposed estimator are examined in terms of key system parameters. The theoretical predictions are demonstrated by means of simulation.

New methods for detecting edges in an image using spatial and scale-space domains are proposed. A priori knowledge about geometrical characteristics of edges is used to assign a probability factor to the chance of any pixel being on an edge. An improved double thresholding technique is introduced for spatial domain filtering. Probabilities that pixels belong to a given edge are assigned based on pixel similarity across gradient amplitudes, gradient phases and edge connectivity. The scale-space approach uses dynamic range compression to allow wavelet correlation over a wider range of scales. A probabilistic formulation is used to combine the results obtained from filtering in each domain to provide a final edge probability image which has the advantages of both spatial and scale-space domain methods. Decomposing this edge probability image with the same wavelet as the original image permits the generation of adaptive filters that can recognize the characteristics of the edges in all wavelet detail and approximation images regardless of scale. These matched filters permit significant reduction in image noise without contributing to edge distortion. The spatially adaptive wavelet noise-filtering algorithm is qualitatively and quantitatively compared to a frequency domain and two wavelet based noise suppression algorithms using both natural and computer generated noisy images.

We propose a fully three-dimensional (3-D) object-based coding system exploiting the diagnostic relevance of the different regions of the volumetric data for rate allocation. The data are first decorrelated via a 3-D discrete wavelet transform. The implementation via the lifting steps scheme allows to map integer-to-integer values, enabling lossless coding, and facilitates the definition of the object-based inverse transform. The coding process assigns disjoint segments of the bitstream to the different objects, which can be independently accessed and reconstructed at any up-to-lossless quality. Two fully 3-D coding strategies are considered: embedded zerotree coding (EZW-3D) and multidimensional layered zero coding (MLZC), both generalized for region of interest (ROI)-based processing. In order to avoid artifacts along region boundaries, some extra coefficients must be encoded for each object. This gives rise to an overheading of the bitstream with respect to the case where the volume is encoded as a whole. The amount of such extra information depends on both the filter length and the decomposition depth. The system is characterized on a set of head magnetic resonance images. Results show that MLZC and EZW-3D have competitive performances. In particular, the best MLZC mode outperforms the others state-of-the-art techniques on one of the datasets for which results are available in the literature.

A conventional color histogram (CCH) considers neither the color similarity across different bins nor the color dissimilarity in the same bin. Therefore, it is sensitive to noisy interference such as illumination changes and quantization errors. Furthermore, CCHs large dimension or histogram bins requires large computation on histogram comparison. To address these concerns, this paper presents a new color histogram representation, called fuzzy color histogram (FCH), by considering the color similarity of each pixel's color associated to all the histogram bins through fuzzy-set membership function. A novel and fast approach for computing the membership values based on fuzzy c-means algorithm is introduced. The proposed FCH is further exploited in the application of image indexing and retrieval. Experimental results clearly show that FCH yields better retrieval results than CCH. Such computing methodology is fairly desirable for image retrieval over large image databases.