A Theory of Shape Identification by Frédéric Cao, José-Luis Lisani, Jean-Michel Morel, Pablo

By Frédéric Cao, José-Luis Lisani, Jean-Michel Morel, Pablo Musé, Frédéric Sur

Recent years have obvious dramatic development match acceptance algorithms utilized to ever-growing photograph databases. they've been utilized to picture sewing, stereo imaginative and prescient, photo mosaics, reliable item reputation and video or internet photograph retrieval. extra essentially, the facility of people and animals to discover and realize shapes is among the enigmas of notion.

The publication describes an entire technique that starts off from a question snapshot and a picture database and yields a listing of the photographs within the database containing shapes found in the question snapshot. A fake alarm quantity is linked to every detection. Many experiments will exhibit that favourite basic shapes or photographs can reliably be pointed out with fake alarm numbers starting from 10-5 to under 10-300.

Technically talking, there are major matters. the 1st is extracting invariant form descriptors from electronic pictures. the second one is identifying no matter if form descriptors are identifiable because the related form or no longer. A perceptual precept, the Helmholtz precept, is the cornerstone of this choice.

These judgements depend upon effortless stochastic geometry and compute a fake alarm quantity. The reduce this quantity, the safer the identity. the outline of the methods, the numerous experiments on electronic photos and the easy proofs of mathematical correctness are interlaced with the intention to make a analyzing available to varied audiences, akin to scholars, engineers, and researchers.

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N This term does not depend upon l. Thus ∞ Pr(nH(µi )Li < ε|Li = l) Pr(Li = l) l=0 Hence, ε n ∞ Pr(Li = l) = l=0 ε . n 24 2 Extracting Meaningful Curves from Images N E i=1 Xi |N = n ε. N ε, which means exactly that the expected This finally implies E i=1 Xi number of ε-meaningful curves is less than ε. ⊓ ⊔ In this proposition, it is not assumed a priori that the Ci are level lines of u. Indeed, in this case it cannot be asserted that the length (number of independent points) of the curve is independent from the values of the gradient along the curve.

3. If p(α, l) > p∗ = 10−3 , reject the piece. α l/2 α∗ = αl/2 , Part II: Greedy algorithm 1. Keep the candidate for which αl/2 is minimal, mark it as flat part, and discard it from the list of candidates. 2. Reject all candidates that meet this best candidate. 3. Iterate until no candidate is available anymore. 4 Some Properties of the Detected Flat Parts The condition defining the candidates (αl/2 < p∗ ) is not a real constraint for long curves. 97 are accepted as candidates. Nevertheless, long pieces of curves often show subparts with a lower probability and a greedy algorithm will therefore prefer them.

Monasse and Guichard proposed to pick the shapes with highest contrast in the shape tree, which is almost the same definition as the one given in [118]. The recent paper [56] proposed an efficient MSER algorithm for real time object tracking in video and in [138] and [166, 167] fast tree computations alternatives and variants to the FLST have also been proposed. In [51] an a contrario technique is used to select shapes in the level lines tree having contrasted enough boundaries. Variations of this technique are [110] and [35].

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