Area minimization problem for convex lattice polygons

Darbā aplūkota problēma par izliektu režģa n-stūru minimālā laukuma atrašanu. Pierādīta teorēma par vienāda laukuma n-stūru klasi un apskatītas tās sekas. Dots izliektu režģa n-stūru ar minimālo laukumu atrašanas algoritms, ka arī tā realizācija ar programmēšanas līdzekļiem.This paper deals with the problem of determining convex lattice polygon with minimum area. The theorem about the set of polygons with equal area has been proved and the consequences of this theorem have been considered as well. The algorithm for determining lattice convex polygon with minimum area is considered. Algorithm realization using programming software is considered as well

On Convex minimal Lattice Polygons, Algorithm for Computing Minimum of Area

Darbā aplūkota problēma par izliekta režģa n-stūra minimālā laukuma a(n) atrašanu. Pierādīta teorēma par vienāda laukuma n-stūru klasi un apskatītas tās sekas. Pierādīts, ka fiksētam n uzdevumu var reducēt uz galīgu pārlasi. Izstrādāts algoritms un ar tā palīdzību aprēķinātas a(n) vērtības, ja n < 21. Iegūti vairāki jauni rezultāti: a(15) = 51,5; a(17) = 75,5; a(19) = 106,5; a(21) = 144,5.This paper deals with the problem of determining convex lattice polygon with minimum area a(n). The theorem about the set of polygons with equal area has been proved and the consequences of this theorem have been considered as well. For fixed n we reduce the problem to finite search. The algorithm has been elaborated and by means of it the values of a(n) have been calculated when n < 21. A several new results have been obtained: a(15) = 51.5; a(17) = 75.5; a(19) = 106.5; a(21) = 144.5

Semi-Supervised Methods to Identify Individual Crowns of Lowland Tropical Canopy Species Using Imaging Spectroscopy and LiDAR

Our objective is to identify and map individuals of nine tree species in a Hawaiian lowland tropical forest by comparing the performance of a variety of semi-supervised classifiers. A method was adapted to process hyperspectral imagery, LiDAR intensity variables, and LiDAR-derived canopy height and use them to assess the identification accuracy. We found that semi-supervised Support Vector Machine classification using tensor summation kernel was superior to supervised classification, with demonstrable accuracy for at least eight out of nine species, and for all combinations of data types tested. We also found that the combination of hyperspectral imagery and LiDAR data usually improved species classification. Both LiDAR intensity and LiDAR canopy height proved useful for classification of certain species, but the improvements varied depending upon the species in question. Our results pave the way for target-species identification in tropical forests and other ecosystems