We show that a rectangle can be signed tiled by ribbon L n-ominoes, n odd, if and only if it has a side divisible by n. A consequence of our technique, based on the exhibition of an explicit Gröbner basis, is...We show that a rectangle can be signed tiled by ribbon L n-ominoes, n odd, if and only if it has a side divisible by n. A consequence of our technique, based on the exhibition of an explicit Gröbner basis, is that any k-inflated copy of the skewed L n-omino has a signed tiling by skewed L n-ominoes. We also discuss regular tilings by ribbon L n-ominoes, n odd, for rectangles and more general regions. We show that in this case obstructions appear that are not detected by signed tilings.展开更多
Let T<sub>n </sub>be the set of ribbon L-shaped n-ominoes for some n≥4 even, and let T<sup>+</sup><sub>n</sub> be T<sub>n</sub> with an extra 2 x 2 square. We investiga...Let T<sub>n </sub>be the set of ribbon L-shaped n-ominoes for some n≥4 even, and let T<sup>+</sup><sub>n</sub> be T<sub>n</sub> with an extra 2 x 2 square. We investigate signed tilings of rectangles by T<sub>n</sub> and T<sup>+</sup><sub>n</sub> . We show that a rectangle has a signed tiling by T<sub>n</sub> if and only if both sides of the rectangle are even and one of them is divisible by n, or if one of the sides is odd and the other side is divisible by . We also show that a rectangle has a signed tiling by T<sup>+</sup><sub>n, </sub> n≥6 even, if and only if both sides of the rectangle are even, or if one of the sides is odd and the other side is divisible by . Our proofs are based on the exhibition of explicit GrÖbner bases for the ideals generated by polynomials associated to the tiling sets. In particular, we show that some of the regular tiling results in Nitica, V. (2015) Every tiling of the first quadrant by ribbon L n-ominoes follows the rectangular pattern. Open Journal of Discrete Mathematics, 5, 11-25, cannot be obtained from coloring invariants.展开更多
We show that the least number of cells (the gap number) one needs to take out from a rectangle with integer sides of length at least 2 in order to be tiled by ribbon right trominoes is less than or equal to 4. If the ...We show that the least number of cells (the gap number) one needs to take out from a rectangle with integer sides of length at least 2 in order to be tiled by ribbon right trominoes is less than or equal to 4. If the sides of the rectangle are of length at least 5, then the gap number is less than or equal to 3. We also show that for the family of rectangles that have nontrivial minimal number of gaps, with probability 1, the only obstructions to tiling appear from coloring invariants. This is in contrast to what happens for simply connected regions. For that class of regions Conway and Lagarias found a tiling invariant that does not follow from coloring.展开更多
针对具有显著对象的彩色图像,尤其是事件和场景等语义简单的商标、地标图像,提出了一种组合特征的图像检索方法。在分析光谱能量结构模型的基础上,将颜色边界用于构建前景对象轮廓直方图,将颜色不变量用于提取对象的局部特征点,提出了...针对具有显著对象的彩色图像,尤其是事件和场景等语义简单的商标、地标图像,提出了一种组合特征的图像检索方法。在分析光谱能量结构模型的基础上,将颜色边界用于构建前景对象轮廓直方图,将颜色不变量用于提取对象的局部特征点,提出了一种结合对象轮廓与对象局部特征点的方法,称之为Freeman码与ORB特征综合法(color invariants to Freeman and ORB,CIFO)。应用CIFO对多组图像进行了实验,结果表明,对于检索具有显著对象的彩色图像,CIFO特征方法比目前基于特征检索的三种经典方法有明显优势。展开更多
提出了一种结合颜色不变量和MROGH(multi-support region order-based gradient histogram)的特殊纹理影像匹配方法。首先在MROGH算法基础上引入颜色不变量模型,构造同时纳入局部影像颜色和空间关系的描述符;然后采用预测同名区域方式...提出了一种结合颜色不变量和MROGH(multi-support region order-based gradient histogram)的特殊纹理影像匹配方法。首先在MROGH算法基础上引入颜色不变量模型,构造同时纳入局部影像颜色和空间关系的描述符;然后采用预测同名区域方式缩小搜索空间;最后采用最小二乘匹配方法精化匹配结果。实验表明,在纹理重复和纹理贫乏区域本文提出影像匹配算法不仅能获取较多匹配点,而且能达到子像素级的影像匹配精度。展开更多
文摘We show that a rectangle can be signed tiled by ribbon L n-ominoes, n odd, if and only if it has a side divisible by n. A consequence of our technique, based on the exhibition of an explicit Gröbner basis, is that any k-inflated copy of the skewed L n-omino has a signed tiling by skewed L n-ominoes. We also discuss regular tilings by ribbon L n-ominoes, n odd, for rectangles and more general regions. We show that in this case obstructions appear that are not detected by signed tilings.
文摘Let T<sub>n </sub>be the set of ribbon L-shaped n-ominoes for some n≥4 even, and let T<sup>+</sup><sub>n</sub> be T<sub>n</sub> with an extra 2 x 2 square. We investigate signed tilings of rectangles by T<sub>n</sub> and T<sup>+</sup><sub>n</sub> . We show that a rectangle has a signed tiling by T<sub>n</sub> if and only if both sides of the rectangle are even and one of them is divisible by n, or if one of the sides is odd and the other side is divisible by . We also show that a rectangle has a signed tiling by T<sup>+</sup><sub>n, </sub> n≥6 even, if and only if both sides of the rectangle are even, or if one of the sides is odd and the other side is divisible by . Our proofs are based on the exhibition of explicit GrÖbner bases for the ideals generated by polynomials associated to the tiling sets. In particular, we show that some of the regular tiling results in Nitica, V. (2015) Every tiling of the first quadrant by ribbon L n-ominoes follows the rectangular pattern. Open Journal of Discrete Mathematics, 5, 11-25, cannot be obtained from coloring invariants.
文摘We show that the least number of cells (the gap number) one needs to take out from a rectangle with integer sides of length at least 2 in order to be tiled by ribbon right trominoes is less than or equal to 4. If the sides of the rectangle are of length at least 5, then the gap number is less than or equal to 3. We also show that for the family of rectangles that have nontrivial minimal number of gaps, with probability 1, the only obstructions to tiling appear from coloring invariants. This is in contrast to what happens for simply connected regions. For that class of regions Conway and Lagarias found a tiling invariant that does not follow from coloring.
文摘针对具有显著对象的彩色图像,尤其是事件和场景等语义简单的商标、地标图像,提出了一种组合特征的图像检索方法。在分析光谱能量结构模型的基础上,将颜色边界用于构建前景对象轮廓直方图,将颜色不变量用于提取对象的局部特征点,提出了一种结合对象轮廓与对象局部特征点的方法,称之为Freeman码与ORB特征综合法(color invariants to Freeman and ORB,CIFO)。应用CIFO对多组图像进行了实验,结果表明,对于检索具有显著对象的彩色图像,CIFO特征方法比目前基于特征检索的三种经典方法有明显优势。
文摘提出了一种结合颜色不变量和MROGH(multi-support region order-based gradient histogram)的特殊纹理影像匹配方法。首先在MROGH算法基础上引入颜色不变量模型,构造同时纳入局部影像颜色和空间关系的描述符;然后采用预测同名区域方式缩小搜索空间;最后采用最小二乘匹配方法精化匹配结果。实验表明,在纹理重复和纹理贫乏区域本文提出影像匹配算法不仅能获取较多匹配点,而且能达到子像素级的影像匹配精度。
