| 26 | | INTRODUCTION |
| 27 | | |
| 28 | | Mathematical morphology (MM) offers a variety of tools for texture char- |
| 29 | | acterization, such as granulometry, morphological covariance, orientation |
| 30 | | maps, etc. The |
| 31 | | rst two in particular have been employed successfully in a |
| 32 | | number of texture analysis applications [3, 7, 22, 23]. |
| 33 | | More precisely, granulometry is a powerful tool based on the "sieving" |
| 34 | | principle, implemented by means of successive openings and/or closings with |
| 35 | | structuring elements (SE) of various sizes, hence it is capable of extracting |
| 36 | | shape and size characteristics from textures. Morphological covariance on |
| 37 | | the other hand, is based on erosions with pairs of points separated by vectors |
| 38 | | of various lengths, and provides information on the coarseness, anisotropy |
| 39 | | as well as periodicity of its input. |
| 40 | | In this paper, we concentrate on these two operators, and speci |
| 41 | | cally on |
| 42 | | the combined exploitation of their SE variables: size, distance and direction. |
| 43 | | Since the original size-only de |
| 44 | | nition of pattern spectra [13], these operators |
| 45 | | have been extended in various ways (e.g., color, multivariate, attribute based |
| 46 | | versions, etc.). Relatively recent applications have explored for instance |
| 47 | | the combination of SE shape and size as far as granulometry is concerned |
| 48 | | [24,25], hence leading to a feature matrix rather than a vector, that describes |
| 49 | | Proceedings of the 8th International Symposium on Mathematical Morphology, |
| 50 | | the combined size and shape distribution of its input. As to covariance, the |
| 51 | | coupled use of SE pair distance and direction makes it possible to exploit the |
| 52 | | anisotropic properties of textures additionally to their periodicity [12, 23]. |
| 53 | | Here we investigate the ways of combining the complementary infor- |
| 54 | | mation extracted by these two operators (e.g., concatenation, dimension |
| 55 | | reduction, etc.), and propose a hybrid of the two, where SE couples are |
| 56 | | varied in terms of size, direction as well as distance. The proposed combi- |
| 57 | | nation scheme is compared in terms of classi |
| 58 | | cation accuracy, against the |
| 59 | | standard de |
| 60 | | nitions, using the publically available Outex13 color texture |
| 61 | | database. The so far obtained experimental results show that it leads to an |
| 62 | | improvement over the usual concatenation of feature vectors. |
| 63 | | Furthermore, as far as the extension of this operator to color images is |
| 64 | | concerned, since MM is based on complete lattice theory, a vector ordering |
| 65 | | mechanism becomes necessary. Hence, we propose a weight based reduced |
| 66 | | vector ordering, de |
| 67 | | ned on the improved HLS (IHLS) color space, designed |
| 68 | | speci |
| 69 | | cally for the purpose of color texture classi |
| 70 | | cation. This approach |
| 71 | | makes it possible to optimize, for instance through genetic algorithms, the |
| 72 | | weight of each component adaptively, according to the training set under |
| 73 | | consideration. |
| 74 | | The rest of the paper is organized as follows. Section 2 introduces brie |
| 75 | | y |
| 76 | | granulometry and covariance, and then elaborates on the combination of |
| 77 | | their variables. In Section 3, the problem of extending morphological op- |
| 78 | | erators to multivariate images is discussed, and the proposed ordering is |
| 79 | | detailed. Next, Section 4 presents the experimental results that have been |
| 80 | | obtained with the Outex13 database. Finally, Section 5 is devoted to con- |
| 81 | | cluding remarks. |
| 82 | | |
| 83 | | |
