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

ISBN-10: 3540684808

ISBN-13: 9783540684800

Recent years have visible dramatic growth fit popularity algorithms utilized to ever-growing picture databases. they've been utilized to picture sewing, stereo imaginative and prescient, photo mosaics, good item attractiveness and video or net picture retrieval. extra essentially, the facility of people and animals to notice and realize shapes is likely one of the enigmas of belief.

The e-book describes an entire strategy that starts off from a question picture and a picture database and yields a listing of the pictures 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 easy shapes or pictures can reliably be pointed out with fake alarm numbers starting from 10^{-5} to below 10^{-300}.

Technically conversing, there are major concerns. the 1st is extracting invariant form descriptors from electronic pictures. the second one is figuring out even if form descriptors are identifiable because the comparable form or no longer. A perceptual precept, the Helmholtz precept, is the cornerstone of this choice.

These judgements depend on straightforward stochastic geometry and compute a fake alarm quantity. The reduce this quantity, the safer the id. the outline of the techniques, the various experiments on electronic pictures and the easy proofs of mathematical correctness are interlaced on the way to make a interpreting obtainable to varied audiences, resembling scholars, engineers, and researchers.

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**Additional resources for A Theory of Shape Identification**

**Sample text**

It divides the image into two connected components: the interior and the exterior of the curve. Let us compute the empirical contrast distribution in each component. Meaningful boundaries are then detected, independently in each connected component. This procedure can now be recursively applied. Since the tree of level lines of a quantized image has a finite depth, it is clear that the detection procedure stops after a finite number of steps. Two problems make things slightly more delicate. First, the order that is used to describe the image boundaries may have an influence.

1 Flat Parts Detection Algorithm Consider a chord from a given curve C: its endpoints delimitate a piece of curve of length l (measured in pixels). n−1} −−−−−−−−−→ → angle(C(si )C(si+1 ), − u) , where the discrete piece of curve is made of the n consecutive points C(si ). Suppose that α is below some fixed threshold α∗ . Following the discussion on independence in Sect. 5, consider that points at a geodesic distance (along the curve) larger than 2 are statistically independent. Thus, there are l/2 statistically independent segments of the type (C(si ), C(si+1 )) along a curve with length l.

What is actually contradicted is our assumption that these exceptional curves do correspond to edges, no matter how small the contrast is. This assumption indeed implies that one is able to distinguish arbitrary gray level changes. This is perceptually not true. 5 Multiscale Meaningful Boundaries The contrast measure is an approximation of the gradient by finite differences. More precisely, Desolneux et al. 7) ∂x 2 ∂u 1 ≃ uy (i, j) = (u(i, j + 1) + u(i + 1, j + 1) − u(i, j) − u(i + 1, j)). 8) ∂y 2 Using a 2×2 scheme is coherent with the application of Helmholtz principle: points at distance 2 have independent values of contrast in white noise.

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

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