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533
The pyramid match kernel: Discriminative classification with sets of image features
 IN ICCV
, 2005
"... Discriminative learning is challenging when examples are sets of features, and the sets vary in cardinality and lack any sort of meaningful ordering. Kernelbased classification methods can learn complex decision boundaries, but a kernel over unordered set inputs must somehow solve for correspondenc ..."
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Cited by 544 (29 self)
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in the number of features, and it implicitly finds correspondences based on the finest resolution histogram cell where a matched pair first appears. Since the kernel does not penalize the presence of extra features, it is robust to clutter. We show the kernel function is positivedefinite, making it valid
Fuzzy histograms and density estimation, in
 SMPS 2006, Third Internat. Workshop on Soft Methods in Probability and Statistics
"... The probability density function is a fundamental concept in statistics. Specifying the density function f of a random variable X on Ω gives a natural description of the distribution of X on the universe Ω. When it cannot be specified, an estimate of this density may be performed by using a sample o ..."
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Cited by 4 (2 self)
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and in counting the number Acck of observations belonging to each cell Ak. If all the Ak have the same width h, the histogram is said to be uniform or regular. Let 1lAk be the characteristic function of Ak, we have
Fuzzy histograms and density estimation
"... The probability density function is a fundamental concept in statistics. Specifying the density function f of a random variable X on Ω gives a natural description of the distribution of X on Ω. When it cannot be specified, an estimate of this density may be performed by using a sample of n observati ..."
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that belong to each cell Ak. If all the Ak have the same width h, the histogram is said to be uniform or regular. Let 1lAk be the characteristic function of Ak, we have
Quasicontinuous histograms
, 2009
"... Histograms are very useful for summarizing statistical information associated with a set of observed data. They are one of the most frequently used density estimators due to their ease of implementation and interpretation. However, histograms suffer from a high sensitivity to the choice of both refe ..."
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Histograms are very useful for summarizing statistical information associated with a set of observed data. They are one of the most frequently used density estimators due to their ease of implementation and interpretation. However, histograms suffer from a high sensitivity to the choice of both
ColorShape Histograms for Image . . .
 IN PROC. OF THE INTL. WORKSHOP ON MULTIMEDIA INFORMATION RETRIEVAL
, 2000
"... Color is a commonly used feature for realizing contentbased image retrieval (CBIR). In this context, this paper presents a new approach for CBIR which is based on well known and widely used color histograms. Contrasting to previous approaches, such as using a single color histogram for the whole ..."
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for the whole image, or local color histograms for a xed number of image cells, the one we propose (named ColorShape) uses a variable number of histograms, depending only on the actual number of colors present in the image, which our experiments have shown often to be low. Our experiments using a large set
The pyramid match kernel: Efficient learning with sets of features
 Journal of Machine Learning Research
, 2007
"... In numerous domains it is useful to represent a single example by the set of the local features or parts that comprise it. However, this representation poses a challenge to many conventional machine learning techniques, since sets may vary in cardinality and elements lack a meaningful ordering. Kern ..."
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Cited by 136 (10 self)
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similarity in time linear in the number of features. The pyramid match maps unordered feature sets to multiresolution histograms and computes a weighted histogram intersection in order to find implicit correspondences based on the finest resolution histogram cell where a matched pair first appears. We show
Consistency of datadriven histogram methods for density estimation and classification
 Annals of Statistics
, 1996
"... We present general sufficient conditions for the almost sure L1consistency of histogram density estimates based on datadependent partitions. Analogous conditions guarantee the almostsure risk consistency of histogram classification schemes based on datadependent partitions. Multivariate data i ..."
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Cited by 54 (4 self)
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We present general sufficient conditions for the almost sure L1consistency of histogram density estimates based on datadependent partitions. Analogous conditions guarantee the almostsure risk consistency of histogram classification schemes based on datadependent partitions. Multivariate data
1Histogram Based Frontier Exploration
"... Abstract—This paper proposes a method for mobile robot exploration based on the idea of frontier exploration which suggests navigating the robot toward the boundaries between free and unknown areas in the map. A global occupancy grid map of the environment is constantly updated, based on which a glo ..."
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global frontier map is calculated. Then, a histogram based approach is adopted to cluster frontier cells and score these clusters based on their distance from the robot as well as the number of frontier cells they contain. In each stage of the algorithm, a sub–goal is set for the robot to navigate. A
Applications of Histogram Principal Components Analysis
"... Abstract. In [8, Rodrı́guez, Diday and Winsberg (2000)], they propose an algorithm for Principal Components Analysis when the variables are of histogram type. This algorithm also works if the data table has variables of interval type and histogram type mixed. If all the variables are interval type ..."
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= max{s, where s is the number of modalities of Y j}, j = 1, 2,..., n where Y j is of histogram type3. We define the vector–succession of intervals associated with each cell of X as: 1. if xij = [a, b] then the vector–succession of intervals associated is: x↓ij = [a, b] [a, b]
Mirror Symmetry Histograms for Capturing Geometric Properties in Images
"... We propose a data structure that captures global geometric properties in images: Histogram of Mirror Symmetry Coefficients. We compute such a coefficient for every pair of pixels, and group them in a 6dimensional histogram. By marginalizing the HMSC in various ways, we develop algorithms for a ra ..."
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Cited by 1 (1 self)
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range of applications: detection of nearlycircular cells; location of the main axis of reflection symmetry; detection of celldivision in movies of developing embryos; detection of wormtips and indirect cellcounting via supervised classification. Our approach generalizes a series of histogram
Results 1  10
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533